Reasoning for Competitive Exams

Syllogism Mega Question Bank

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 10:47:00 +0000

PRACTICE TEST

Directions (Q. 1-71): In each question below there are three statements followed by four conclusions numbered, I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the

given statements, disregarding commonly known facts.

1. Statements:

a. No Cloud is Bird.

b. Some Goats are Birds.

c. All Cars are Goats.

Conclusions:

I. No Car is Cloud.

II. Some Cars are Birds.

III. No Bird is Car.

IV. Some Clouds are Goats.

1) Only III follows

2) Only either II or III follows

3) Only I follows

4) Only I and either II or III follow

5) None of these

2. Statements:

a. All Grapes are Bananas.

b. All Potatoes are Bananas.

c. Some Bananas are Mangoes.

Conclusions:

I. No Grape is Mango.

II. Some Potatoes are not Mangoes.

III. Some Grapes are Potatoes.

IV. All Mangoes are Grapes.

1) Only I follows

2) Either I or III follows

3) Only II & III follow

4) Only I, II & III follow

5) None of these

3. Statements:

a. Some Cats are Rats.

b. Some Rats are Ants.

c. Some Ants are Flies.

Conclusions:

I. Some Flies are Cats.

II. Some Flies are not Ants.

III. No Rat is Fly. IV.No Cat is Fly.

1) Only I & IV follow 2) Only II follows

3) Only I & III follow

4) Only I or IV follows

5) None of these

4. Statements:

a. All Chalks are Dusters

b. Some Chalks are Boards.

c. Some Dusters are Pens.

Conclusions:

I. Some Pens are Chalks.

II. Some Dusters are Boards.

III. Some Pens are Boards.

IV. All Chalks are Pens.

1) Either I or IV follows 2)Only II & III follow

3) Either I or IV & II follow

4) Only II follows 5) None of these

5. Statements:

a. Some Bags are Books.

b. All Books are Boxes.

c. No Box is Board.

Conclusions:

I. Some Bags are not Boards.

II. Some Bags are not Boxes.

III. All Bags are Boxes.

IV. No Bag is Board.

1) Only I follows

2) I & either II or III folk

3) Only IV follows

4) Only II follows

5) None of these

6. Statements:

Some streets are roads.

Some roads are lanes.

Some lanes are highways.

Conclusions:

I. Some roads are not streets.

II. No highway is street.

III. Some streets are not roads.

IV. Some lanes are not roads.

1) Only III follows

2) Only IV and III follow

3) Either I or III follows

4) Both I and III follow

5) None of these

7. Statements:

Some pencils are pens.

All pens are erasers.

All staplers are erasers.

Conclusions:

I. Some pens are not pencils.

II. All erasers are pencils.

III. Some staplers are pens.

IV. Some staplers are pencils.

1) Only I follows 2) Only II follows

3) Only III follows 4) Only IV follows

5) None of these

8. Statements:

Some tables are chairs.

No cupboard is table.

Some chairs are cupboards.

Conclusions:

I. Some chairs are not tables.

II. All chairs are either tables or cupboard

III. Some chairs are both tables and

cupboards.

IV. All chairs are tables.

1) Only I and IV follow

2) Only either II or III follow

3) Only IV follows

4) Either II or III & I follow

5) None of these

9. Statements:

All birds are animals.

Some animals are humans.

All humans are mammals.

Conclusions:

I. Some humans are not birds.

II. Some birds are humans.

III. Some animals are not mammals.

IV. All animals are mammals.

1) Only I and II follow

2) Either III or IV follows

3) Either I or II follows

4) Either I or II and either III or IV follow

5) None of these

10. Statements:

Some leaves are fruits.

All branches are fruits.

Some roots are branches

Conclusions:

I. Some roots are fruits.

II. Some branches are leaves.

III. No leaf is branch.

IV. Some leaves are roots.

1) Either II or III and I follow

2) Only I follows

3) Only either II or III follows

4) Only I and III follow

5) None of these

11. Statements:

All books are notes.

Some notes are pencils.

No pencil is paper.

Conclusions:

I. Some notes are books.

II. Some pencils are books.

III. Some books are papers.

IV. No book is a paper.

1) Only I follows

2) Only I and either III or IV follow

3) Either III or IV follows

4) Only I and III follow

5) None of these

12. Statements:

Some cups are utensils.

No utensil is a bucket.

All buckets are plates.

Conclusions:

I. Some cups are buckets.

II. Some utensils are plates.

III. No utensil is a plate.

IV. Some cups are plates.

1) Only I follows

2) Only III follows

3) Either II or III follows

4) Either III or IV follows

5) None of these

13. Statements:

Some keys are locks.

All locks are doors.

Some doors are windows.

Conclusions:

I. Some locks are windows.

II. Some windows are keys.

III. Some windows are doors.

IV. No window is a lock.

1) Either I or IV follows

2) Only II follows

3) Only III and IV follow

4) None follows

5) None of these

14. Statements:

All pins are staplers.

Some staplers are sharpeners.

Some sharpeners are stands.

Conclusions:

I. Some staplers are stands.

II. Some sharpeners are pins.

III. Some pins are stands.

IV. Some stands are sharpeners.

1) Only I and II follow

2) Only II and IV follow

3) Only III follows

4) Only IV follows

5) None of these

15. Statements:

Some oranges are apples.

All apples are guavas.

No guava is a banana.

Conclusions:

I. Some guavas are oranges.

II. No apple is a banana.

III. Some oranges are bananas.

IV. Some apples are bananas.

1) Only I and II follow

2) Only I and either II or IV follow

3) Only I, II and IV follow

4) Only III and either II or IV follow

5) None of these

16. Statements:

Some spectacles are boxes.

No bat is a ball.

Some boxes are balls.

Conclusions:

I. Some boxes are not bats.

II. Some bats are spectacles.

III. No bat is a box.

IV. No ball is a spectacle.

1) Only I follows

2) Only 1 & III follow

3) Only II and III follow

4) Only IV follows

5) None of these

17. Statements:

All fans are tubelights.

No pen is a bulb.

Some bulbs are fans.

Conclusions:

I. Some pens are tubelights.

II. No pens are tubelights.

III. Some tubelights are fans.

IV. All tubelights are fans.

1) Only I and II follow

2) Only I, II and III follow

3) Either I or II and III follow

4) Only III and IV follow

5) None of these

18. Statements:

Some fruits are vegetables.

All liquids are drinks.

All drinks are fruits.

Conclusions:

I. Some drinks are vegetables.

II. Some fruits are liquids.

III. All liquids are fruits.

IV. No liquids are vegetables.

1) Only I and II follow

2) Only II and III follow

3) Only III and IV follow

4) Only I, II & III follow

5) None of these

19. Statements:

All shirts are trousers.

Some socks are shoes.

All shoes are shirts.

Conclusions:

I. Some socks are shirts.

II. Some socks are trousers.

III. All shoes are trousers.

IV. All shoes are socks.

1) Only I and II follow

2) Only I or II or III follows

3) Only II and IV follow

4) Only III and IV follow

5) None of these

20. Statements:

Some books are papers.

All plates are records.

Some records are books.

Conclusions:

I. Some plates are books.

II. Some records are papers.

III. Some papers are plates.

IV. Some books are records.

1) Only I follows

2) Only II and III follow

3) Only I and III follow

4) Only IV follows

5) None of these

21. Statements:

Some ice are ring.

No ring is paint.

Some rings are gold.

Conclusions:

I. No gold is paint.

II. No ice is gold.

III. Some rings are paints.

IV. All golds are rings.

1) Only I and III follow

2) Only I and II follow

3) Only III and IV follow

4) Only II and III follow

5) None of these

22. Statements:

All gates are flowers.

Some gates are fruits.

Some flowers are clips.

Conclusions:

I. Some flowers are fruits.

II. Some clips are fruits.

III. Some clips are gates.

IV. No flower is fruit.

1) Only I follows

2) Only I and IV follow

3) Only II and IV follow

4) Only I and III follow

5) None of these

23. Statements:

No candle is bell.

Some shoes are bells.

All tables are shoes.

Conclusions:

I. Some tables are bells.

II. No table is bell.

III. Some shoes are candles.

IV. No shoe is a candle.

1) Only I and IV follow

2) Only I and II follow

3) Only III and IV follow

4) Only II and IV follow

5) None of these

24. Statements:

Some films are clouds.

All rats are clouds.

Some clouds are chairs.

Conclusions:

I. No film is chair.

II. Some rats are films.

III. Some clouds are rats.

IV. Some chairs are rats.

1) Only I and III follow

2) Either II or IV follows

3) No conclusion follows

4) Only IV follows

5) None of these

25. Statements:

Some cups are slates.

All slates are apples.

No apple is a car.

Conclusions:

I. Some cars are slates.

II. Some cups are cars.

III. Some apples are cups.

IV. No car is a cup.

1) Only II follows 2) Only III follows

3) Only IV follows 4) Either II or IV & III

follow 5) None of these

26. Statements:

All buds are bells.

Some buds are cakes.

Some bells are sponges.

Conclusions:

I. Some cakes are sponges.

II. Some bells are buds.

III. Some sponges are not cakes.

IV. Some bells are not sponges.

1) Only either 1 or III and II follow

2) Only II and III follow

3) Only I and IV follow

4) Only either I or IV and II follow

5) None of these

27. Statements:

No machine is a fly.

Some flies are colours.

All colours are sweets.

Conclusions:

I. Some machines are colours.

II. All sweets are colours.

III. Some sweets are flies.

IV. No sweet is a machine.

1) Only either II or IV and III follow

2) Only I and II follow 3) Only IV follows

4) Only III follows 5) None of these

28. Statements:

Some kings are cars.

Some cars are bottles.

No bottle is a lemon.

Conclusions:

I. Some cars are lemons.

II. No king is a lemon.

III. Some kings are bottles.

IV. All cars are either kings or bottles.

1) Only I and II follow

2) Only either 1 or II and III follow

3) Only III or IV follows

4) Only IV follows

5) None of these

29. Statements:

Some goats are hammers.

All hammers are diamonds.

No diamond is green.

Conclusions:

I. No goat is green.

II. Some diamonds are hammers.

III. Some goats are diamonds.

IV. Some greens are hammers.

1) Only I and IV follow

2) Only II and IV follow

3) Only II and III follow

4) Only either II or III and I follow

5) None of these

30. Statements:

Some cars are mopeds.

Some mopeds are hills.

All pencils are mopeds.

Conclusions:

I. All pencils are hills.

II. Some pencils are cars.

III. Some cars are hills.

IV. Some pencils are not cars.

1) Only I follows

2) Only either II or IV follows

3) Only I or III follows

4) Only I and IV follow

5) None of these

31. Statement:

Some pages are papers.

Some papers are magazines.

All magazines are books.

Conclusions:

I. Some books are magazines.

II. Some books are papers.

III. Some magazines are pages.

IV. Some pages are magazines.

1) All follow

2) Only I and III follow

3) Only II and IV follow

4) Only I and IV follow

5) None of these

32. Statements:

All windows are doors.

No door is a lock.

Some locks are keys.

Conclusions:

I. Some locks are doors.

II. Some locks are not doors.

III. Some keys are not doors.

IV. All doors are windows.

1) All follow

2) Only either I or II follows

3) Only either I or II and III follow

4) None follows

5) None of these

33. Statements:

Some shirts are coats.

All coats are jackets.

Some jackets are trousers.

Conclusions:

I. Some shirts are jackets.

II. Some jackets are shirts.

III. All trousers are jackets.

IV. Some trousers are jackets.

1) All follow

2) Only I, II and III follow

3) Only I, II and IV follow

4) Only II, III and IV follow

5) None of these

34. Statements:

All bikes are scooters.

All scooters are scooties.

All scooties are mopeds.

Conclusions:

I. All mopeds are scooties.

II. All scooties are scooters.

III. All scooters are bikes.

IV. All bikes are mopeds.

1) None follows 2) All follow

3) Only III and IV follow4) Only IV follows

5) None of these

35. Statements:

Some pots are buckets.

Some buckets are bags.

Some bags are purses.

Conclusions:

I. Some purses are buckets.

II. Some bags are pots.

III. Some purses are pots.

IV. Some pots are bags.

1) All follow 2) None follows

3) Only I and III follow

4) Only II and IV follow

5) None of these

36. Statements:

All biscuits are chocolates.

Some chocolates are breads.

All breads are pastries.

Conclusions:

I. Some biscuits are pastries.

II. Some pastries are chocolates.

III. Some biscuits are not pastries.

IV. All pastries are breads.

1) Only I and II follow

2) Only I, II and III follow

3) Only either I or III and II follow

4) Only either I or III and IV follow

5) None of these

37. Statements:

All glasses are roads.

No road is a stick.

Some sticks are pens.

Conclusions:

I. Some glasses are sticks.

II. Some pens are sticks.

III. Some roads are sticks.

IV. No glass is a stick.

1) None follows

2) Only I or IV and II follow

3) Only either I or II and IV follows

4) Only either I or II and IV follow

5) None of these

38. Statements:

Some lions are goats.

Some goats are horses.

Some horses are flowers.

Conclusions:

I. Some lions are horses.

II. Some goats are flowers.

III. Some lions are flowers.

IV. Some horses are lions.

1) None follows

2) All follow

3) Only I and IV follow

4) Only II and III follow

5) None of these

39. Statements:

All trees are books.

Some books are tables.

All tables are pencils.

Conclusions:

I. Some pencils are tables.

II. Some books are trees.

III. Some tables are trees.

IV. Some pencils are trees.

1) None follows 2) All follow

3) Only either I or III follows

4) Only either I or II follows

5) None of these

40. Statements:

Some doors are windows.

All windows are dogs.

Some dogs are cats.

Conclusions:

I. Some dogs are doors.

II. All dogs are doors.

III. Some cats are windows.

IV. Some dogs are windows.

1) Only I and II follow

2) Only II and III follow

3) Only I and IV follow

4) All follow

5) None of these

41. Statements:

All buses are trains.

All trains are rickshaws.

All rickshaws are cycles.

Conclusions:

I. All cycles are buses.

II. All rickshaws are buses.

III. All buses are rickshaws.

IV. All trains are cycles.

1) All follow 2) None follows

3) Only I and II follow

4) Only II and III follow

5) None of these

42. Statements :

Some bricks are trees.

All trees are pens.

All pens are boats.

Conclusions:

I. Some boats are bricks

II. Some pens are bricks

III. Some trees are bricks

IV. Some bricks are boats

1) None follows 2) All follow

3) Only I and II follow

4) Only III and IV follow

5) None of these

43. Statements:

All cups are tables.

No table is water.

Some waters are clothes.

Conclusions:

I. No cloth is cup. II. No cloth is table.

III. Some clothes are waters.

IV. Some waters are cups.

1) None follows 2) All follow

3) Only III follows 4) Only I and II follow

5) None of these

44. Statements:

Some flowers are rods.

Some rods are doors.

Some doors are houses.

Conclusions:

I. Some houses are flowers.

II. Some doors are flowers.

III. Some flowers are doors.

IV. No house is flower.

1) Only I and IV follow

2) Only II and III follow

3) Only either I or II follows

4) Only either I or IV follows

5) None of these

45. Statements:

All trucks are vans.

All vans are cars.

All cars are trains.

Conclusions:

I. All trains are trucks.

II. All cars are trucks.

III. All trucks are trains.

IV. All vans are trains.

1) All follow 2) Only I and II follow

3) Only II and III follow 4) Only II and IV

5) None of these

46. Statements:

No table is fruit.

No fruit is window.

All windows are chairs.

Conclusions:

I. No window is table.

II. No chair is fruit.

III. No chair is table.

IV. All chairs are windows.

1) None follows 2) All follow

3) Only I and II follow 4) Only III & IV follow

5) None of these

47. Statements:

All birds are fruits.

Some fruits are towers.

All towers are windows.

Conclusions:

I. Some birds are towers.

II. Some windows are birds.

III. Some windows are fruits.

IV. Some towers are birds.

1) None follows 2) Only I and II follow

3) Only II and III follow 4) Only III follows

5) All follow

48. Statements:

Some buses are trains.

No train is a dog.

All dogs are parrots.

Conclusions:

I. No bus is a parrot.

II. Some parrots are trains.

III. Some parrots are buses.

IV. No dog is a bus.

1) Only either I or III follows

2) Only II follows 3) Only IV follows

4) Only I and III follow 5) None of these

49. Statements:

Some cups are flowers.

Some flowers are boxes.

All boxes are tigers.

Conclusions:

I. Some tigers are cups.

II. Some tigers are flowers.

III. Some boxes are cups.

IV. No tiger is a flower.

1) None follows

2) Only either II or IV follows

3) Only III follows

4) Only either I or III follows

5) None of these

50. Statements:

Some cats are lions.

All lions are hares.

All hares are horses.

Conclusions:

I. Some cats are horses.

II. Some horses are lions.

III. Some hares are cats.

IV. Some cats are hares.

1) Only I and II follow

2) Only III and IV follow

3) Only I and III follow

4) All follow

5) None of these

51. Statements:

All boats are rivers.

All rivers are mangoes.

All mangoes are apples.

Conclusions:

I. All apples are boats.

II. All mangoes are boats.

III. All rivers are apples.

IV. All boats are apples.

1) All follow

2) Only I and II follow

3) Only I, III and IV follow

4) Only II, III and IV follow

5) None of these

52. Statements:

a. Some boxes are trees.

b. Some trees are horses,

c. All horses are fruits.

Conclusions:

I. Some fruits are boxes.

II. Some fruits are trees.

III. Some horses are boxes.

IV. No fruits are boxes.

1) None follows

2) Only either II or IV follows

3) Only either I or IV and II follow

4) Only either I or III and IV follow

5) None of these

53. Statements:

a. All flowers are buses.

b. Some buses are cats.

c. All cats are tigers.

Conclusions:

I. Some tigers are buses.

II. Some tigers are flowers.

III. Some cats are flowers.

IV. Some buses are tigers.

1) None follows

2) Only I and II follow

3) Only III and IV follow

4) Only I and IV follow

5) Only II and III follow

54. Statements:

a. All fans are rooms.

b. No room is green.

c. Some windows are green.

Conclusions:

I. Some windows are fans.

II. Some windows are rooms.

III. Some fans are green.

IV. No green is fan.

1) Only I follows 2) Only III follows

3) Only IV follows 4) Only II & IV follow

5) All follow

55. Statements:

a. Some tablets are rains.

b. All dogs are rains.

c. All rains are chairs.

Conclusions:

I. Some chairs are tablets.

II. All dogs are chairs.

III. Some tablets are dogs.

IV. Some tablets are chairs.

1) All follow 2) Only I, II&III follow

3) Only II, III and IV follow

4) Only III & IV follow 5) None of these

56. Statements:

a. No man is sky.

b. No sky is road.

c. Some men are roads.

Conclusions:

I. No road is man.

II. No road is sky.

III. Some skies are men.

IV. All roads are rnen.

1) None follows 2) Only I follows

3) Only 1 and III follow 4) Only II & III follow

5) None of these

57. Statements:

a. Some candles are houses.

b. Some houses are trains.

c. Some trains are roads.

Conclusions:

I. Some roads are candles.

II. Some trains are candles.

III. Some roads are houses.

IV. Some candles are roads.

1) None follows 2) All follow

3) Only I and II follow 4) Only II & III follow

5) Only III and IV follow

58. Statements:

a. No tree is fruit.

b. All fruits are stones,

c. All stones are rains.

Conclusions:

I. No stone is tree. II. No rain is tree.

III. Some rains are fruits.

IV. Some rains are trees.

1) None follows

2) Only either II or IV and III follow

3) Only either II or III and I follow

4) All follow 5) None of these

59. Statements:

a. All books are stars.

b. Some stars are windows,

c. All windows are hills.

Conclusions:

I. Some windows are books.

II. Some hills are stars.

III. Some hills are books.

IV. Some stars are books.

1) None follows 2) Only I & III follow

3) All follow 4) Only II & IV follow

5) None of these

60. Statements:

a. Some cats are rats,

b. All rats are bats,

c. Some bats are jungles.

Conclusions:

I. Some jungles are cats.

II. Some bats are cats.

III. Some jungles are rats.

IV. No jungles is cat.

1) None follows

2) Only III follows

3) Only either I or IV and III follow

4) Only either I or IV and II follow

5) None of these

61. Statements:

a. All flowers are clouds.

b. No clouds is sky

c. All skies are tigers.

Conclusions:

I. Some clouds are flowers.

II. All clouds are flowers.

III. Some tigers are skies.

IV. All tigers are skies.

1) Only II and IV follow

2) Only either I or II follows

3) Only either III or IV follows

4) All follow 5) None of these

62. Statements:

a. Some dogs are rats.

b. All rats are trees.

c. Some trees are not dogs.

Conclusions:

I. Some trees are dogs.

II. All dogs are trees.

III. All rats are dogs.

IV. All trees are dogs.

l) None follows 2) Only I follows

3) Only I and II follow 4) Only II & III follow

5) All follow

63. Statements:

a. Some boys are rains.

b. All rains are clouds.

c. Some clouds are cars.

Conclusions:

I. Some clouds are boys.

II. Some cars are boys.

III. Some cars are rains.

IV. Some rains are boys.

1) None follows 2) Only IV follows

3) Only I follows 4) Both I & IV follow

5) All follow

64. Statements:

a. All bricks are flowers.

b. Some houses are flowers.

c. All pens are houses.

Conclusions:

I. Some houses are bricks.

II. Some pens are flowers.

III. Some flowers are bricks.

IV. No pen is flower.

1) Only either II or IV and III follow

2) Only either II or IV and I follow

3) Only either I or II and IV follow

4) None follows 5) All follow

65. Statements:

a. All lions are ducks.

b. No duck is a horse.

c. All horses are fruits.

Conclusions:

I. No lion is a horse.

II. Some fruits are horses.

III. Some ducks are lions.

IV. Some lions are horses.

1) All follows

2) Only either I or II and both III and IV follow

3) Only either I or IV and both II and III follow

4) Only either I or IV and II follow

5) None of these

66. Statements:

a. Some mountains are rivers.

b. Some rivers are roads.

c. Some roads are windows.

Conclusions:

I. Some windows are roads.

II. Some rivers are mountains.

III. Some roads are mountains.

IV. Some windows are rivers.

1) All follow 2) Only I and II follow

3) Only III and IV follow4) Only I & IV follow

5) None follows

67. Statements:

a. All benches are trees.

b. All trees are flowers.

c. All flowers are fruits.

Conclusions:

I. All fruits are benches.

II. All trees are fruits.

III. Some fruits are flowers.

IV. Some flowers are benches.

1) All follow

2) Only II,III& IV follow

3) Only III and IV follow

4) Only II & III follow

5) None of these

68. Statements:

a. Some trains are radios.

b. Some radios are waters.

c. All tigers are waters.

Conclusions:

I. Some trains are tigers.

II. Some trains are waters.

III. No water is train.

IV. All waters are tigers.

1) None follows 2) Both II & III follow

3) Only either II or III follows

4) Only either I or III follows

5) Only either I or IV follows

69. Statements:

a. Some buses are rivers.

b. All rivers are mountains.

c. Some roads are mountains.

Conclusions:

I. Some mountains are buses.

II. Some roads are buses.

III. Some roads are rivers.

IV. Some mountains are roads.

l) None follows 2) Only I and II follow

3) Only III and IV follow4) Only I & IV follow

5) All follow

70. Statements:

a. All lions are jungles.

b. Some jungles are rabbits.

c. All rabbits are elephants.

Conclusions:

I. Some rabbits are lions.

II. Some elephants are jungles.

III. Some elephants are lions.

IV. Some elephants are rabbits.

1) Only I and III follow 2) Only I and II follow

3) Only II and III follow 4) Only III & IV follow

5) None of these

71. Statements:

a. All books are pens.

b. No pens are houses.

c. All houses are doors.

Conclusions:

I. No books are houses.

II. No books are doors.

III. Some doors are pens.

IV. Some houses are books.

1) Only I follows 2) Only I and II follow

3) Only II and III follow
4) Only III & IV follow

5) None of these

Coded Relations

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 09:23:00 +0000

Coded Relations is another important topic for Bank Exams. You can easily get 5 marks with little logical thinking and concentration. It doesn't take much effort to solve these type of questions... All that you need is Concentration and lil practice to solve these type of questions

1. If 'A X B' means 'A is the Daughter of B'. 'A + B' means 'A is the husband of B' and 'A - B' means ' A is the sister of B', then what does ' M + N - P X Q' Mean?

Sol :

M + N - P X Q => M is the Husband of N, N is the sister of P and P is the Daughter of Q.

N and P are sisters and the daughters of Q. Q is either mother or father of N and P. so M is Son-In-Law to Q.

Have a look at the below image for more clarifications.

Directions (2-3): Study the following information carefully and answer the questions given below.

' P X Q' means 'P is Sister of Q'

' P + Q' means 'P is mother of Q'

'P - Q' means 'P is father of Q'

'P % Q' means 'P is brother of Q'

2. Which of the following represents 'A is nephew of B'?

A % B - C
C % B - A
C X B + A X D
C % B - A % D
None of the Above

Sol :

A is nephew of B means, A must be MALE. The symbols '-' and '%' indicate the male Gender. So, A must be followed by either '-' or '%'. So, checking of options 1 and 4 will be enough to solve this question.

1. A % B - C => A is brother of B and B is father of C. Here, A is C's paternal Uncle.

4. C % B - A % D => C is brother of B, B is father of A and A is brother of D. So here, A is son of B.

So the answer is, 5. None of the Above

3. Which of the following represents 'W is Grand Father of H'??

W + T - H
W % T - H
W X T + H
W % T + H
None of these

Sol:

W is Grand Father of H means W must be a Male. The symbols '-' and '%' indicate the Male Gender. So, W must be followed by Either '-' or '%'. So, Obviously we have to check the options 2 and 4.

2. W % T - H => W is brother of T and T is father of H. Here, W is paternal uncle to H.

3. W % T + H => W is brother of T and T is mother of H. W is maternal uncle of H.

So the answer is, 5. None of these

Directions (4-5) : Following questions are based on the information given below.

'P X Q' means 'P is father of Q'

'P - Q' means 'P is sister of Q'

'P + Q' means 'P is mother of Q'

'P%Q' means 'P is brother of Q'

4. Which of the following represents 'J is son of F'?

J % R - T X F
J + R - T X F
J % M - N X F
Cant Say
None of the above

Sol:

J is son of F means J must be a Male. So, J must be followed by the symbols 'X' or '%". We have to check options 1 or 3.

1. J % R - T X F => J is brother of R, R is sister of T and T is father of F. So, J is paternal uncle of F.

3. J % M - N X F => J brother of M, M is sister of N and N is father of F. Here, J is paternal uncle of F.

5. In the expression B + D X M % N, how is M related to B?

SOn
Grand Daughter
Grand Son
Grand Daughter or Grand Son
None of the above

Sol:

B + D X M % N =>B is mother of D, D is father of M and M is brother of N. M is Grand Son of B.

Blood Relation-Set 2

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 09:16:00 +0000

POINTS TO REMEMBER :

If the question is "How is A related to B". Then you must know the gender of A to answer the question

Without knowing A's gender, you cannot determine the relation from A to B

If a person is Uncle or Aunt to "A", A is that person's nephew (if A is Male) or niece (if A is female)
Cousin is a common Gender (I mean, you can use this word for both Male and Female)

Ex : A says to B, "you are the son of my grand father's only son".

How is B related to A?
How is A related to B?

Ans :

B is Brother of A.

My grand father's only son = A's father (grand father's only son means only ONE son.. No other son and no daughter also)

A is either brother or sister to B

A and B are siblings. B is brother to A as we know the Gender of B. But we dont know the Gender of A. So we cant say whether A is Brother or Sister to B.

Lets have a look at some practice problems :

The mother of Ranbir is the only daughter of Neetu's father. How Neetu is related to Ranbir?

Sister
Mother
Aunt
Cant determine
None of These

Answer : Mother

Explnation : Only daughter of Neetu's father = Neetu only.

The mother of Ranbir is Neetu, so Neetu is the mother of Ranbir :D

Ex 1. ) Amit is the son of Ajit's grand father's only daughter. How is Ajit's father related to Amit?

Grand Father
Uncle
Father
Data Inadequate
None of these

Answer : Father

Explanation : Ajit's grand father's only daughter means Ajit's mother. Amit is the son of Ajit's mother. So, Amit and Ajit are Siblings. Ajit's father is Amith's father too

Ex 2. )Pointing to a boy Rekha said, "He is the son of my mother-in-law's only Child". How is the boy related to Rekha?

Son
Grand Son
Nephew
Brother
Cant determined

Ans : Son

Explnation : My mother-in-law's only child = Rekha's mother-in-law's only child = Rekha's husband.The boy is the son of the Rekha's Husband. So obviuosly Rekha is the mother to that boy and that boy is the Son of Rekha.

Ex 3. )B is the husband of C. A is the sister of B. D is the sister of C. How is D related to B?

Uncle
Sister-in-Law
Cant be determined

Ans : Sister-in-Law

Explnation :

B is Husband and C is his Wife.
A is the sister of B, so A is the Sister-in-Law of C ( Husband's sister)
D is the sister of C so, D is the Sister-in-Law of B (Wife's Sister)

Ex 4. ) Pointing towards a girl, a Person said, "She is the only daugher of the only son of the wife of the father-in-law of my wife". How is the girl related to the Person?
Niece
Daughter
Sister
Daughter-in-Law
Cant be Determined

Ans : Daughter

Explnation :

Father-in-Law of my wife = Father in Law of the Person's Wife = Person's Father
Wife of the Father-in-law of my wife = Wife of the Person's Father = Person's Mother.
Only son of Person's Mother = That Person only (because Person's parents dont have any other child)
So, she is the only daughter of Person as the Person does not have any other Children.

AdvanceVerbal Analogy Questions

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 09:05:00 +0000

1."Bank" is related to "Money" in the same way as "Transport" is related to ?

Movement

Road

Speed

Traffic

Goods?

Answer 5) Goods.

Explanation :A bank deals with transaction of 'money', where as the 'transport' deals with the movement of 'goods'

2."Horse" is related to "Hoof" in the same way as "Eagle" is related to ?

Leg

Clutch

Claw

Foot

None of the above

Answer 3) Claw.

Explanation :The lower part of feet of "Horse" is know as "Hoof", where as lower part of feet of "Eagle" is called as "Claw".

3. "Marriage" is to "Divorce" as "True" is to ?

Truth

Story

Fiction

False

None of the above

Answer 4) False

Explanation :"Divorce" is the antonym of "Marriage". In the same way "False" is the antonym of "True".

4.Leaf is related to Sap in the same way as Bone is related to ?

Marrow

Fluid

Blood

Calcium

None of the above

Answer 1) Marrow

Explanation :Sap is the fluid contained in Leaf in the same way marrow is the fluid contained in Bone.

5.Which of the following pairs of words bears the same relationship as that of the pair of words given at the question place?

Cells : Cytology :: Insects :

Ornithology

Entomology

Anatomy

Onomatology

None of the above

Answer 2) Entomology

Explanation :Cytology is the study of Cells and Entomology is the study of Insects. (Extra info : Ornithology is the study of Birds, Anatomy is the study of the structure of human or animal bodies and Onomatology is the study of Names)

6.What is found once in Tea, Twice in Coffee, but not in milk?

Water

Cream

Sugar

"E"

None of the above

Answer 3) "E"

Explanation :The English alphabet "E" is found once in the word "Tea", twice in the word "Coffee" and there is no such alphabet in the word "Milk"

7. Always : Never ::

Frequently : Normally

Intermittently : Casually

Rarely : Casually

Constantly : Frequently

Often : Rarely

Answer 5) Often : rarely

Explanation :"Always" and "Never" are antonyms in the same way "Often" and "Rarely" are also antonyms.

8.Bull is related to Draught in the same way Cow is related to ?

Milch

Livestock

Farm

Fodder

None of the above

Answer 1) Milch

Explanation :Bull is a draught animal (beast of burden) and cow is a milch animal (milk - yielding)

9.A "Square" is related to "Cube" in the same way as "Circle" is related to

Sphere

Circumference

Diameter

Area

None of The above

Answer 1) Sphere

Explanation :A square is a two dimensional figure consisting of sides where as a cube is a three dimensional figure. Similarly, circle is a two dimensional figure and a sphere is a three dimensional figure.

10. "Iron" is related to "Solid" in the same way as "Mercury" is related to ?

Vapour

Solid

Gas

Liquid

None of the above

Answer 4) Liquid

Explanation :Iron is found in solid state. Similarly, mercury is found in liquid state.

11. "12" is related to "36" in the same way as "17" is related to ?

Answer is 5) 51

Explanation :Three times of 12 is equal to 36 (12 X =3 = 36). Similarly, three times of 17 is equal to 51 (17 X 3 = 51).

13."Horse" is related to Hay in the same way as Cow is related to ?

Milk

Leaves

Straw

Fodder

None of the above

Answer 4) Fodder

Explanation :Hay is the food of horse. Similarly, Fodder is the food of Cow.

14. Horse : Hoof :: Cat : ?

Horns

Wings

Legs

Mane

Paws

Answer 5) Paws

Explanation :Hoof is the name of the feet of horse. Similarly, Paws is the name of the feet of the Cat

15.Swan is related to Cygnet in the same way as Fish is related to ?

Fry

Fawn

Fin

Foal

None of the above

Answer 1)Fry

Explanation :Here Fry means not the Fish Fry :P Fry is the name of the baby fish :)

16. Cygnet is the young one of Swan in the same way as fry is the young one of Fish.

Young is related to Old in the same way as wide is related to ?

Big

Insufficient

Long

Narrow

None of these

Answer d) Narrow

Explanation :The words in ach pair are antonyms of each other.

17.Tempest is to storm as slim is to ?

Slender

Plump

Fat

Beautiful

Stout

Answer 1) Slender

Explanation :First is of higher intensity than the second

How to Solve Verbal Analogy Problems

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 07:36:00 +0000

Which Strategy Should be followed to solve Verbal Analogy Problems ?

The first step in analysing original analogous pair of words (the head pair) is to describe the connection between the words of the pair. The best way to do this is to formulate a sentence that express the connection between the words. Since the purpose of this sentence is to analyse or diagnose the nature of the connection between the words. Since the purpose of this sentence is to analyse or diagnose the nature of the connection between the words of the head pair, we may call it Diagnostic Sentence or DXS for short.
After formulating the DXS, test each answer choice to find the pair of words that best fit the sentence.

Consider the following example

ECSTASY : PLEASURE ::

hatred : affection
condemnation : approval
rage : anger
difficult : understanding
privacy : invasion

Now, the first step is to formulate a DXS. ECSTASY means "great or overwhelming PLEASURE," so the DXS might be "ECSTASY is extreme PLEASURE"

The second step is to test each of the answer choices with the DXS.

....................is extreme....................

Hatred is extreme affection
Condemnation is extreme approval
Rage is extreme anger
Difficulty is extreme understanding
Privacy is extreme invasion

Here, option 3 is the best answer. Because for only Option 3, the pair of words correctly fit the DXS.

Now lets have a look at another example.

ACCIDENTAL : INTENTION ::

Voluntary : Requirement
Anticipated : Performance
Interesting : Feeling
Practical : Knowledge
Insane : Connection

DXS : Somethign that is ACCIDENTAL is done without INTENTION.

Now, test each of the answer choices with the diagnostic sentence.

Something that is ............ is done without .........................

Something that is voluntary is done without requirement
Something that is anticipated is done without performance
Something that is interesting is done without feeling
Something that is practical is done without knowledge
Something that is insane is done without connection

here option 1 is the answer, and it is the only logical substitution that makes scene in this DXS.

More Solved Examples
Each question consist of two words which have a certain relationship to each other followed by four pairs of related words, Select the pair which has the same relationship.

1. DIVA:OPERA
A. producer:theatre B. director:drama
C. conductor:bus D. thespian:play

Answer: Option D

2. GRAIN:SALT
A. shard:pottery B. shred:wood
C. blades:grass D. chip:glass
Answer: Option D

3. THRUST:SPEAR
A. mangle:iron B. scabbard:sword
C. bow:arrow D. fence:epee
Answer: Option D

4. PAIN:SEDATIVE
A. comfort:stimulant B. grief:consolation
C. trance:narcotic D. ache:extraction
Answer: Option B

5. LIGHT:BLIND
A. speech:dumb B. language:deaf
C. tongue:sound D. voice:vibration
Answer: Option A

6. WAN:COLOUR
A. corpulent:weight B. insipid:flavour
C. pallid:complexion D. enigmatic:puzzle
Answer: Option B

7. PORK:PIG
A. rooster:chicken B. mutton:sheep
C. steer:beef D. lobster:crustacean
Answer: Option B

8. AFTER:BEFORE
A. first:second B. present:past
C. contemporary:historic D. successor:predecessor
Answer: Option D

9. INDIGENT:WEALTHY
A. angry:rich B. native:affluent
C. gauche:graceful D. scholarly:erudite
Answer: Option C

10. DISTANCE:MILE
A. liquid:litre B. bushel:corn
C. weight:scale D. fame:television
Answer: Option A

11. TEN:DECIMAL
A. seven:septet B. four:quartet
C. two:binary D. five:quince
Answer: Option C

12. MUNDANE:SPIRITUAL
A. common:ghostly B. worldly:unworldly
C. routine:novel D. secular:clerical
Answer: Option B

13. ARMY:LOGISTICS
A. business:strategy B. soldier:students
C. war:logic D. team:individual
Answer: Option A

14. GRAVITY:PULL
A. iron:metal B. north pole:directions
C. magnetism:attraction D. dust:desert
Answer: Option C

15. FILTER:WATER
A. curtail:activity B. expunge:book
C. edit:text D. censor:play
Answer: Option D

16. HOPE:ASPIRES
A. love:elevates B. film:flam
C. fib:lie D. fake:ordinary
Answer: Option C

17. CORPOREAL:SPIRITUAL
A. mesa:plateau B. moron:savant
C. foreigner:immigrant D. pedagogue:teacher
Answer: Option B

18. SYMPHONY:COMPOSER
A. Leonardo:music B. Fresco:painter
C. colours:pallet D. art:appreciation
Answer: Option B

Mathematical Operations Using BODMAS RULE

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 07:14:00 +0000

For Reasoning Section with Mathematical Operations, all calculations will be performed using BODMAS Rule. We can divide these problems in three types.Those are,

Symbol Substitution
Mathematical Logic
Interchange of Signs & Numbers

Now lets discuss these types with detailed examples.

1st Type : Symbol Substitution

In this type, to find the value of the given expression you should replace the symbols by mathematical operations. Then apply the BODMAS Rule (i.e., Brackets, of, Division, Multiplication, Addition, Subtraction).

For the detailed understanding, lets have a look at an example

Example : 42% (9-2) + 6 x 3 - 4

Solution :
42 % (9-2) + 6 x 3 - 4
= 42 % 7 + 6 x 3 - 4
= 6 + 6 x 3 - 4
= 6 + 18 - 4
= 24 - 4 = 20

2nd Type : Mathematical Logic

In this type, they just give you some logical statements followed by some mathematical operations. You should solve the given mathematical operations with the help of given logical statements.

Example : If % stands for greater than, x stands for addition, + stands for division, - stands for equal to, > stands for multiplication, = stands for less than, < stands for minus, then which of the following alternatives is correct ?

3 + 2 < 4 % 6 > 3 x 2
3 x 2 < 4 % 6 + 3 < 2
3 > 2 < 4 - 6 x 3 x 2
3 x 2 x 4 = 6 + 3 < 2

Usually for these type of questions people tend to make direct decisions with the help of given statements. But confusion arises when you tried to coordinate given mathematical symbols with the logical statements mentioned above. It is because lack of coordination between eyes and brain. So, to avoid confusion you just should make a note of given logical statements in simple mathematical equations format. So that it will be easier for your eye to pick the correct operation.

Solution : Using the symbols correctly as given in the above operations, for the option (2) you will get, 3+2-4>6%3-2. Using BODMAS rule in this inequality, we will get 5-4>2-2 or, 1>0, which is correct.

3rd Type : Interchange of Signs & Numbers

In this type they just give you some random set of numbers and mathematical symbols. And then ask you to choose the correct of symbols to fit the given equation.

Example : Select the correct set of symbols which will fit in the given equation 5 0 3 5 = 20

x, x, x
=, +, x
x, +, x
+, -, x

Solution : Using the set of symbols given in options, you will get the Option 2 as the correct answer.

Using the set of symbols given in option 2, you will get the equation,

5-0+3x5 = 20

Using BODMAS rule you will get,

5-0+15=20 or 20-0 = 20 which is correct

Now lets have a look at some examples,

1. '<' means subtraction, '>' means Addition, '+' means Multiplication and '$' means Division. Then what will be the value of 27 > 81 $ 9 < 6 ?

Solution :

27+81%9-6 = 27+9-6 = 36-6 = 30

2. If % means +, - means x, x means -, + means %, then what will be the value of 15 - 2 % 900 + 90 x 100 ?

Solution :

15x2+900%90-100 = 30 + 10 - 100 = -60

3. Q means Addition, J means Multiplication, T means Subtraction, K means Division then what is the value of 30K2Q3J6T5 ?

Solution :

3%2+3x6-5 = 15 + 18 - 5 = 28

4. P means x, R means +, T means %, S means -, then what will be the value of 18T3P9S8R6 ?

Solution :

By substituting the given symbols, you will get the answer 52

5. P means Multiplication, T means Subtraction, M means Addition, B means Division then what will be the value of 28B7P8T6M4 ?

Solution :

28 % 7 x8 - 6 + 4

= 4 x 8 - 6 + 4

= 32 - 6 + 4

= 36 - 6 = 30

Odd Man Out- AlphabetSeries

noreply@blogger.com (Anonymous) — Mon, 01 Dec 2014 07:04:00 +0000

Classification / Odd Man out Series is one of the important topic in Reasoning Section. To made the concepts clear, we've divided this topic into 3 sections.

Those are

Alphabets
Numbers
Words.

Single Alphabets :

If single alphabets are given, then you should follow the order of checking

Vowels first. If you are unable to figure odd ones, then check for
mirror images, later
water images and finally check for the
place values so that you may get any clues with the number associated with that specific alphabet.

Example Problems :

Solution : Obviously here the answer is A. Because its the only Vowel in the list.

Solution : Here the answer is H. Because, the Difference between alphabets is 2.

Solution : Here the Odd one is H, because it is the only Mirror Image in the List. (There are 2 water images D and H)

Alphabet Groups

If multiple Alphabets are given, you should follow the order of checking,

Alphabetical order of given alphabets
Distance / Gap between the given alphabets
Vowel / Consonant differences

Example Problems :

ABC
BCD
CDE
DEF
EFG

Solution : :

Check the Order : ABC... BCD... CDE... DEF... EFG... Well, here all alphabets are in an order.. So we cant find out the Odd one with this logic.

Check the Gap : All alphabets carrying equal number differences / Gaps.. So this technique too of no use.

Check for the Vowels.

In the group 1, One vowel is there (A)
In the group 2, No vowel
In the group 3, One vowel is there (E)
In the group 4, One vowel is there (E)
In the group 5, One vowel is there (E)

So, answer should be the Group with NO VOWELS.. Group 2

Here you should note that AE are the only vowels in the given group. So maximum number of people choose Option 1 as their answers. BUT, according to our order given above, we should first check for the alphabetical order... no clue..... later GAP. Check the difference fro Ato E and G to M ....

AbcdE

GhijklM

MnopQ

VwxyZ

LmnoP

Here, except the second pair all the remaining pairs are having 3 letters in between the given alphabets. But the second pair consists of 5 alphabets between G and M. So this is the Odd one. So the answer is Option 2 (not Option 1).

Solution :

Here all the given pairs are having ONE LETTER between them. So now we shall check those alphabets for clue. e, u, w, o, i.. .Here except w all the remaining alphabets are vowels. So, obviously the odd one is the 3rd pair.

AFH
AHL
AJM
ARW
ANR

Well this is little complected one... have a close look... We can't find anything with Alphabetical order.. So try GAPs...

A _ _ _ _ F _ H

A _ _ _ _ _ _ H _ _ _ L

A _ _ _ _ _ _ _ _ J _ _ M

A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ R _ _ _ _ W

A _ _ _ _ _ _ _ _ _ _ _ _ N _ _ _ R

So,

A 4 F 1 H

A 6 H 3 L

A 8 J 2 M

A 16 R 4 W

A 12 N 3 R No Clue :(

Try adding the numbers we got in gaps.....

4+1 = 5

6+3 = 9

8+2 = 10

16+4 = 20

12+3 = 15 No Clue :(

Subtract the numbers,

4-1 = 3

6-3 = 3

8-2 = 6

16-4 = 12

12-3 = 9 No Clue :(

Multiply the numbers

4*1 = 4

6*3 = 18

8*2 = 16

16*4 = 64

12*3 = 36 ................

hey see, are you able to figure out anything?

All numbers except 18 are square numbers. So option 2 is the Odd one.

And remember, for the purpose of explanation, we gave detailed step by step procedure here. For in your exam hall, you should figure out the option / procedure in a single glance. With good practice only you can achieve that state.

ACF
ADI
AGG
AFW
AEO

Solution :

A 1 C 2 F

A 2 D 4 I

A 5 G 25 G (Note : After Z you should again start with A and continue your counting)

A 4 F 16 W

A 3 E 9 O

With a glance, we can find out that

2's square is 4
5's square is 25
4's square is 16
and 3 's square is 9

So, here the odd one is the Option 1.

Solution : Here except Option 1 (VT) all remaining alphabets are in alphabetical order. VT is in reverse order. So this is the ODD one.

Solution : Here, except the 5th option, all the remaining groups having VOWELs (O, U, E, I) in the second position. But the 5th group contains VOWEL (A) in the first position. So, it is the Odd one.

Solution : Here, except the 4th group, all the remaining groups contains only 3 alphabets between them. But the 4th group has 4 alphabets between M and R.

Solution : 3rd groups is reverse in Alphabetical order. So, it is the odd one.

NQV
HKP
RWZ
JMR
KNS

Solution :

N 2 Q 4 V
H 2 K 4 P
R 4 W 2 Z
J 2 M 4 R
K 2 N 4 S

Here obviously the Odd one is option 3.

Brain Teaser # 3

noreply@blogger.com (Anonymous) — Tue, 10 Jan 2012 11:54:00 +0000

Four friends - Mallika, Rakhi, Kashmira and Mahek were comparing the number of sheep that they owned.
It was found that Kashmira had ten more sheep than Mahek. If Mallika gave one-third to Rakhi, and Rakhi gave a quarter of what he then held to Kashmira, who then passed on a fifth of his holding to Mahek, they would all have an equal number of sheep.
How many sheep did Mahek possess?

Options:
a) 45 b)55 c)65 d)50 e)35

Brain Teaser #2

noreply@blogger.com (Anonymous) — Tue, 10 Jan 2012 11:49:00 +0000

A contractor had employed 100 labourers for a flyover construction task. He did not allow any woman to work without her husband. Also, atleast half the men working came with their wives. He paid five rupees per day to each man, four ruppes to each woman and one rupee to each child. He gave out 200 rupees every evening.
How many men were working with the constructor?

a) 20 b)24 c)52 d)72 e)16

Assumptions

noreply@blogger.com (Anonymous) — Tue, 10 Jan 2012 11:26:00 +0000

Assumptions

An assumption is defined as something which is assumed, supposed or taken for granted. In real life, when someone says something, he does not put everything into words. He leaves a lot of things unsaid, which he takes for granted, which may be defined as an assumption. Implicit means hidden; therefore Implicit Assumptions are those assumptions which are hidden. A typical question on implicit assumptions goes like this:

Directions: In each of the questions below, a statement is followed by two assumptions numbered I and II.An assumption is something supposed or taken for granted. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement.

Mark answer 1 if the assumption I is implicit; Mark 2 if only assumption II is implicit;

Mark 3 if either I or II is implicit; Mark 4 if neither I nor II is implicit

and Mark 5 if both I and II are implicit.

Statement: “In my opinion, you should get training from an experienced person in order to succeed in life”, X to Y.

Assumptions: I.Y had asked for advice from X.

II. Experienced persons are better able to guide a person to the path of success.

The correct answer to the question is 2 i.e. only II is implicit but not I. I is not an implicit assumption because there are many examples in real life when we get advice from a person which we have not asked for. So in this light, I is not definitely valid. But II certainly follows from the statement because if it had not been so, X would not have advised Y to get training from an experienced person. Therefore, it is correct to assume that experienced people make better guides.

Statement: “This CD - ROM is meant to help you learn computers without a teacher”. — an ad in a paper.

Assumptions: I. Everyone may not be able to get help from a teacher.

II. Computers can be learnt with the help of a CD-ROM.

In the above, both I and II are valid. The CD-ROM intends to teach computers in the absence of a teacher.This means that the absence of a teacher is a distinct possibility for some people.

Therefore I is valid. The advertiser has come out with a CD-ROM on computers, it definitely implies that he feels that computers can be learnt by CD-ROMs. Hence II is also valid.

Statement: Miss Yukta Mookhey of Bombay has won the Miss Universe contest held in Honolulu.

Assumptions: I. The result of the Miss Universe contest is out.

II. The Honolulu Government always permits the holding of such contests.

Now,in this example, I is definitely implied, otherwise, how do we come to know that Yukta has won the contest? The validity of II is doubtful because the statement mentions or implies this fact nowhere. The Honolulu Government may be unfavorable towards such ideas, but could have agreed on the contest this time only. So far, nothing can be derived about the attitude of the Honolulu Government on the basis of the main statement. Therefore, II is not 100% justifiable. Hence, it is not a valid assumption.

STAND-OUT WORDS IN ASSUMPTIONS

Many words used in assumptions can delineate the scope of their meaning. Some of these Stand-Out Words are Only, All,Definitely, Certainly, Strongly, Best, Worst, Exclusively, Most Certainly,Usually, Rarely, Probably etc. The list here is not exhaustive. But you can get a feel of the point by practicing with such sentences.

Statement: The standard of Indian sports has fallen to abysmal levels and we should make every effort to improve the training facilities for sportspersons

Assumptions: The trend of the falling standards of Indian sports will probably be arrested by improving training facilities.

Undoubtedly,if the writer of the statement is saying that training facilities should be improved in the context of falling standards, it certainly follows that better training should result in an improvement in standards. The assumption is most likely true. But pause for a moment. If the word definitely had been used instead of probably, our assumption would have been invalid because it is not clear from the statement whether training is the only thing responsible for the falling standards of sports.

Statement: The common man’s position remains pitiable despite a massive cut in taxes.

Assumptions: The common man’s position is usually expected to improve as a result of a massive cut in taxes.

The above assumption is valid. Remember this format (when a particular event does not usually occur when another one occurs—indicated by words Even, Despite, In spite of,Notwithstanding, Although, Though)

SOME MORE ASSUMPTIONS

Statement: India will not achieve economic prosperity unless it adopts the free economy model.

Assumption: At the moment,India does not have a free-economy model in operation

The above is case of a valid assumption. The word unless indicates ‘as long as it is not there’. All such assumptions are valid.

Statement: Poor people often face a harsh life.

Assumption: There are poor people in the world.

This again is a case of a valid assumption. If poor people do not exist at all, how can we speak of what kind of life they lead? It implies they must exist for the main statement to be true. That is why this assumption is definitely valid.

Statement: His jovial disposition often leads people to brand him as non-serious.

Assumption: One’s true intentions may be misread by other people.

This assumption says ‘may be’ which does not imply a 100% case. But it is very much possible as illustrated by the main statement. Therefore, this is a valid assumption.

Statement: Since you lack talent, you cannot be admitted to this programme.

Assumption: Talent is essential for admission to the programme.

This type of assumption may be classified as ‘cause-and-effect’ type. In this case, the cause is the presence of talent and admission is the effect, which takes place because of talent. In this case, the assumption is valid.

Statement: Although the maximum security cover was provided to the visiting President, yet it could not prevent the mischief from occurring.

Assumption: The maximum security cover is usually sufficient to prevent any mischief.

You can see for yourself that the above assumption is a valid one in the light of the statement.

Statement: In a psychology experiment, a dog, unable to exercise any control on its surroundings because it was tied to a harness, soon developed ulcers. This proves that the cause of ulcers in humans is the lack of control.

Assumption: Humans and dogs behave similarly in similar situations.

This is a case of using similar situations and extending the results of one situation to the other. We call it assumption by analogy. In the above, the assumption made is a valid one.

In case of advertisements/public notices/appeals, the following standard assumptions apply.

1. The ad/appeal/notice does have some effect.

2. In ads, the thing highlighted is desired/expected/looked for by people.

3. For a public notice, the issuing body has the duty of issuing such notices.

4. In case of a public-notice, the advice given must be beneficial or must be reducing the harm caused otherwise.

5. In case of a notice, the results of implementing it will be useful for the issuing body.

6. In the context of an appeal, there are reasons for issuing that appeal.

Now look at the following examples.

Statement: “India bazaar.com _ the only portal that lets you shop under one roof for all your daily needs – right from needles to noodles.”An ad in a paper.

Assumptions: I. The ad will motivate the readers to buy from the portal

II. People do not like to go from shop to shop looking for their daily necessities.

In the light of the above discussion, I is valid. II is also valid in this case because if people desire to go from shop to shop looking for necessities, the advertiser would not have highlighted the one-stop shop he is offering.Therefore, sufficient reasons exist to justify the validity of the second statement also.

Statement: “Every worker in this company will report in time from tomorrow onwards”- a company notice.

Assumption: I.Workers have the ability to understand the notice.

II. Reporting in time is good for the company’s performance.

Now you can logically conclude that both of the above assumptions are valid.

Statement: “Please count your cash carefully before leaving the cash counter” - a notice at a bank counter.

Assumption: I. It is the duty of the bank to ensure that people get correct amounts of cash whenever they make a transaction at the bank.

II. Unless forewarned, people may not count the cash and may take it to be their correct amount.

In this case again, both the assumptions are valid.

INVALID ASSUMPTIONS

So far, our discussions have focussed on finding valid assumptions. There are certain broad parameters which can help you identify invalid assumptions straightway. In the following section, we will discuss the parameters which can help us sift the invalid assumptions from the valid ones.

Statement: Travel Air-India for Comfort, Timeliness and Economy--An ad in a paper

Assumption: Air-India is the only airline operating there.

It can be easily deduced that the assumption is invalid because the statement does not say or imply that this is the only airline operating in that area.Therefore it can be rejected.

Statement: Airtel is the finest cellphone service in India.

Assumption: All other cellphone services except Airtel are inferior to it.

This assumption is merely a restatement or rephrasal (saying the same thing indifferent words) of the what has been said in the statement. Therefore, it can be rejected straightway. Remember, a re-statement is never a valid assumption.

Statement: Internet is useful to all.

Assumption: Internet is not useless to any one.

Again this is an example of re-statement. Therefore, we can reject it straightway as an invalid assumption.

An assumption will be classified as invalid if it is an inference or conclusion derived on the basis of the main statement. An assumption is something on which the main statement is based while an inference is itself based on the main statement.Look at the following example

Statement: Appeals to people to donate generously for a cause are useless if one does not practice what one preaches.

Assumption: Practicing something which one preaches is essential for achieving that thing.

Now this is a conclusion which follows from the main statement. And since we are looking for assumptions, we can reject it straightway as an invalid assumption.

Statement: The Income-Tax Department has introduced a simplified system for filing returns by the assessees.

Assumption: I. The assessees will welcome the new step.

II. The Income-Tax authorities had studied the oldsystem carefully before discarding it.

Both of these are far-fetched conclusions, which arenot justified by the main statement. They appear be probably correct, but they are quite far-fetched. Therefore, they can be rejected as invalid assumptions straightway.

Brain Teaser: #1

noreply@blogger.com (Anonymous) — Mon, 28 Nov 2011 07:57:00 +0000

There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m.The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

Options
a) 100 m b) 150 m c) 125m d) 120.71m e) 100m

Odd Man Out

noreply@blogger.com (Anonymous) — Mon, 28 Nov 2011 07:27:00 +0000

This is an easy topic, comparatively speaking.In this type of question, there are four or five options, out of which you have to choose, which one is odd i.e. which one is not related to others. In this case, the odd object could be based on an elementary feature, even or odd,gender, use and the applicability of the object. This concept can be made clear with some examples.

Directions: In each of the following questions, find the word, which is least like the others.

Example No. 1: Ram, Sham, Mohan, Seeta

Solution:Here in this case, it can be seen the odd would be Seeta on the basis of gender.

Example No. 2: Car, Jeep, Aeroplane, Bus.

Solution:In this case, the odd object would be airplane, because the rest three move on the road, but the airplane does not. This is odd on the basis of the elementary feature.

Example No. 3: 13, 17, 83, 45.

Solution:In this case, the odd would be 45, which is not a prime number and the rest of the three are a prime number.

Example No. 4: Book, Paper, Pencil and Sharpener.

Solution:Here all the items given are stationery items except book, therefore book is the answer.

Example No. 5: Carrot, Tomato, Ginger, Lemon.

Solution:Here all the vegetables grow underground except lemon. Therefore lemon is the answer.

Example No. 6: Chandigarh, Gangtok, Gandhinagar, Surat.

Solution:Here all the cities given are state capitals except Surat. Thus Surat is the answer.

Example No. 7: Cap, Helmet, Hat, Veil.

Solution: Here all the objects given cover the head, except veil, which covers the face and is the answer.

Example No. 8 : Ladyfinger, Strawberry, Plum, Mango.

Solution:Here all the objects are fruits except Ladyfinger, which is a vegetable.

Example No. 9: Broker, Salesman, Customer, Hawker.

Solution:In this case, all the persons are sellers to the customer except the customer.

Example No. 10: Correction, Improvement, Elevation, Betterment.

Solution: All others are something done to improve except elevation.

Questions of Membership (Set) -II

noreply@blogger.com (Anonymous) — Mon, 28 Nov 2011 07:25:00 +0000

Type– 2:This is another type of question based on logical diagram, known as venn diagram.In this type, various items and their relationships are represented by circles/rectangles/squares. In these questions, you will be presented with three different classes or groups of familiar objects and will be asked to identify their mutual relationships. In short, it deals with questions which aim at analyzing a candidate’s ability to relate certain given groups of items and represent it diagrammatically.

Example No. 1:Lawyers, Mechanics, Doctors

Solution: These three categories have no relation among them.These should be represented by three different diagrams having no intersection at all, as shown below.

Example No. 2: Females, Sisters, Mothers

Solution: These three categories have a relation in such a way that all the sisters and mothers are females, but some of the sisters could be mothers or some of the mothers could be sisters. Therefore the relationship would be as shown below.

Example No. 3:Planets, Earth, Jupiter

Solution: Both Earth and Jupiter are planets, but they both are different and cannot touch each other. So this relationship can be represented in the following manner.

Example No. 4: Doctors, Cats, Humans

Solution: Clearly it can be seen that all the doctors are humans. This should be represented by one circle inside the other circle. But the cats are outside both these categories, so, they should be represented by a different circle. So the relationship can be shown by the following diagram.

Exampleno. 5:Prime Numbers, Natural Numbers, Integers.

Solution: In this case, all the prime numbers are natural numbers and all the natural numbers are integers. So it can be best represented by the following diagram.

ExampleNo. 6:Doctors, Females, Mothers

Solution: This relationship goes like this: all the mothers are females but all the females are not necessarily mothers. Now females can be doctors but all the females are not doctors, similarly all the mothers are not doctors but some can be doctors. Hence this relationship can be best represented by the following diagram.

ExampleNo. 7:Horses, Pets, Dogs

Solution:Clearly, some dogs and some horses are pets,but all the pets are not necessarily dogs or horses. Secondly dogs and horses are not related to each other. Therefore the relationship can be best represented as

ExampleNo. 8:Females, married females, married persons.

Solution: In this case, all the married females are females as well as married persons, but all the females are not married persons, but some can be, similarly all the married persons are not females, but some definitely are. So the relationship can best be represented by the following diagram.

Questions of Membership (Set)

noreply@blogger.com (Anonymous) — Mon, 28 Nov 2011 07:12:00 +0000

These questions take relatively lesser time to solve,allowing one to have greater accuracy. In these questions, you are required to define the relationship diagrammatically between the two or three contents given. The questions in this case are based upon the knowledge of universal facts.

In such questions, the candidate is expected to establish a relationship among three or more items represented by diagrams.This requires a logical understanding and careful observation of the diagrams.The items represented by the diagrams may be individuals, groups,class/category of individuals, or some other phenomenon. Generally two types of questions are asked in this category. Given below are some questions of the first type.

Type I: In this case, three/four categories are given in terms of diagram followed by four or five questions based on those categories.Let us take an example. The triangle represents the urban, the circle represents the educated and the rectangle represents hardworking.

This above-mentioned diagram will giveyou the idea of how you are supposed to answer the questions in this case.

Example No. 1:The following questions are based on the diagram given below where each rectangle represents a class of people:

1) College Students 2)Artists 3) Dancers

a) College students who are artists but not dancers are represented by …………..

Solution: It can be seen that the students (in rectangle no. 1) and artists (in rectangle no. 2) but not dancers (not in rectangle no. 3) is represented by the letter B and is the right answer.

b) Artists who are neither dancers nor college students are represented by …………….

Solution: In rectangle no. 2 but not in 1 and 3 and this is represented by the letter F.

c) College students who are dancers but not artists are represented by …………….

Solution: In rectangle no. 1 and 3 but not in rectangle no. 2 and this is represented by the letter D.

d) College students who are artists as well as dancers are represented by ……………

Solution: It means the part which is common to all the three rectangles and this is represented by the letter N.

e) College students who are neither dancers nor artists are represented by …………….

Solution: It means the part, which is inside rectangle no. 1 but not in rectangle no. 2 and in rectangle no. 3. This is represented by the letter M and is the right answer.

EXAMPLE2:Refer to the following diagram and answer the questions given thereafter.

The rectangle represents Married Employees.

The Triangle represents Urban people.

The circle represents Post Gradates.

The square represents Workers.

1. Which of the following statements is true?

A. All married employees are workers.

B. Some married employees are postgraduates as well as workers.

C. All married employees are postgraduates.

D. All workers are married employees but not postgraduates.

Solution: The above cases may be considered as follows:

For statement A to be true, the rectangle should lie inside the square, this is not true, hence A is false.

For statement B to be true there should be a region common to the rectangle, circle and the square. Such a region is 6.Hence B is true.

For statement C to be true, the rectangle should lie inside the circle, so C is false.

For statement D to be true, the square should lie wholly inside the rectangle, with no region common to the circle,this is not true. So D is false.

2. Which of the following statement is true?

A. All urban people are postgraduates.

B. All workers are married employees but not urban people.

C. All married employees all workers.

D. Some urban people are not postgraduates.

Solution: For the validity of condition A, the triangle should lie inside the circle. This is not true.

So, A is false.

For the validity of statement B, there should be a region which is common to the square and the rectangle but is not apart of the triangle. Since no such region exists, B is false.

For the validity of statement C, the rectangle should lie inside the square. This is not true. So C is false.

For the validity of statement D, do me region of the triangle should lie outside the circle. Since this is true.

3. Choose the correct statement:

A. Some workers are married employees.

B. No worker is urban people.

C. All postgraduates are urban people.

D. All postgraduates are married employees.

Solution: For the validity of statement A, there should be a region common to the square and rectangle. Such regions are 6 and 7. So, A is true.

Further, for statement B to be true,there should be no region common to the square and the triangle. But since the square lies wholly inside the triangle, B is false.

For statement c) to be true, circle should lie inside the triangle. Clearly, C is false.

For the validity of statement d), the circle should lie inside the rectangle. Clearly Dis false.

Direction Sense

noreply@blogger.com (Anonymous) — Wed, 23 Nov 2011 07:15:00 +0000

Questions on directional reasoning are a favorite with all examiners. You will find questions of this type in all almost all reasoning tests. Broadly speaking, the questions on this topic may be categorized into these types:

NORTH-SOUTH-EAST-WEST TYPE:

For purposes of convenience, always remember these four directions, irrespective of where a person starts from (i.e., whether house, office, park or any street),these directions will remain the same. And also, the starting point will always be the intersecting point of these two lines as shown in the figure alongside.Keeping this thing in mind, let us try to solve this poser.

EXAMPLE: A person starts from his office and goes 100 metre towards north. After turning to his right, he walks 50 metre. Thereafter, he again turns right and walks 100 metre. In which direction and at what distance is he from his office now?

In this case, we have to do as has been dictated by the examiner. First of all, he asks us to move 100 meter towards north. Thereafter, he asks us to move to our right, i.e. the east. Again, he requires us to move to our right, i.e.downwards towards the south. As illustrated in the figure alongside, a rectangle is formed consisting of two sides 100 meter and 50 meter. Obviously,the person is 50 meters way from his starting point and at the moment, he is in the eastern direction

EXAMPLE : Mallika starts from home and walks 80 metre towards the south. She turns to her left and walks 50 meters. She again turns to her right and walks 40 metre. She takes a turnt owards her left and walks 60 metre. She takes a final turn towards her left and walks 120 metre. Our problem now is to find her distance and direction from the starting point.

As usual, our starting point will be the point where the N-S and E-W lines intersect, as has been illustrated above. We follow her movement as has been asked of us in the question and finally arrive at a point in the east. Now the problem before us is to find her distance from the starting point. We will have to calculate it indirectly because there is no direct way to do so. If you look carefully, the two distances i.e. 50 and 60 metres joined together give us the distance travelled by her on the eastern side, taken from the starting point.If you transpose this line connecting 50 and 60 meters, you will see that this is exactly the distance traveled by her on the eastern side. So the answer in this case is 100 metres east.

Much commoner is a type involving application of the Pythagorean theorem. Let’s examine such a case.

EXAMPLE: Bhanu starts from her office in the morning at 9 a.m. to meet her friend Kanu. She walks 40 metre towards the west, then takes a right turn and walks 30 metres. What is her distance from thestarting point and in which direction is she now? Now this is posing a bit difficult question. As you can see for yourself, Bhanu is somewhere in the middle of the western and the northern direction. This is where the Pythagorean theorem comes into play. Look carefully, these two distances, 40 and 30 metres, are forming a right-angled triangle, if you supply the third side yourself as has been done alongside.

Just for repetition, the Pythagorean theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the perpendicular and the base.

Letus assume that the third (unknown) side is designated X. Applying the theorem,

X²= (30)² + (40)²

X²= 900 + 1600 = 2500

Therefore, X = Ö2500 = 50 metre. As you can see, she is in the middle of the northern and the western sides. Therefore, combining these two sides, we say that she is at present in the north-west 50 metres away from her starting point.

EXAMPLE:

There is a town called Timbkatoo, the streets of which intersect each another at right angles. Chandu starts from his house in the morning at 9 a.m. and walks 10 metres towards the south. After taking aturn to his left, he travels 20 metres before turning to his right and moves another 30 metres. Thereafter, he travels 20 metre to his left and funnily takes a left turn and travels 50 metre. He reaches a point X. Simultaneously, Saraswati starts from the same point from which Chandu had started. She goes 20 metres tothe west before she turns to her left and walks 10 metre. Thereafter, she takes a right turn, walks 30 metres.Thinking that she has come in the wrong direction, finally, she turns to her right and walks 50 metre to reach point Y. You have to find out at what distance is Saraswati from Chandu?

To find out the distance between X and Y, we simply have to add up the horizontal distance as indicated by the arrows i.e. 10 m + 20 m + 20 m +20 m = 70 m, which is the correct answer.

Let’s imagine a case in which we are asked the distance between Y and the point from which Chandu had taken his last turn. To find this out, we should know the distance between X and Y (70 metre). The third side is the diastase between X and the point from which Chandu had taken his last turn (which is 50 m). From these two, we can calculate the hypotenuse of the right-angled triangle as indicated above by applying the Pythagorean theorem. Our answer comes out to be

One important precaution to be exercised in all such questions is that whenever a person takes a right or left turn, the movement must be presumed to be at 90 degrees to either of the N-S or E-W lines, unless specified otherwise. For example, if in a hypothetical case, a person first walks 15 meter towards the north side and then takes a right turn and walks 20 meter, the movement has to be assumed like this, not otherwise unless it has been specified.

Tricky Number Series: Solved Examples with Explanation

noreply@blogger.com (Anonymous) — Tue, 22 Nov 2011 07:29:00 +0000

Wrong Number Series: Sometimes, a question is asked to find out the wrong number in a series. This is a bit difficult task. This is because from the point where you get a wrong number, all other succeeding numbers would also be look wrong. You can only solve such a question comfortably only if you have expertise in handling the questions on series very well. See the following example.

Example No. 1: Find the wrong number in the following series.

15 46 63 71 75 77 78

Solution: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.

Example No. 2: Find the wrong number in the following series.

10 21 43 85 175

Solution:In this question, the logic involved is ´ 2 + 1 only.But the error lies where instead of 43 ´ 2 + 1 = 87, 85 has been given. So 85 is the wrong number.

* Replacing the Wrong Number: Sometimes, the question is related to not only finding the wrong number, but also with finding the number which should replace the wrong number identified. You can see the following example.

Example No. 3: In the following series, a wrong number is given. Find out that wrong number, and decide which option should replace that wrong number.

1 4 8 9 25 16 64

Solution: In this sequence, two consecutive series are going simultaneously relating to perfect cubes and perfect squares respectively. Firstly 1 cube is given, then 2 cube is given,then 3 cube should have been there which should be 27, but 27 is written at that place. And then there is the cube of 4, i.e 64. And the series given is alternately square of 2, then square of 3 and then square of 4 and so on. You may note this that in order to increase the confusion, the wrong number is also a perfect square.

Example No. 4: In the following series, a wrong number is given. Find out that wrong number, and decide which option should replace that wrong number.

Solution: In this question the series is related to + 2, + 3, + 4 and then there is + 4 again, then + 7, it seems odd. Instead of second + 4 there should be + 5. This means 14 + 5 => 19, should be there instead of 18. And thereafter, the series would become + 6 and + 7 and it would be a right logical series. So 19 is the answer.

Twin Series: This is a newly included type of series in which two series are given, and below that the starting point of another series is given. Now you are supposed to analyze the logic from the first series and apply the same logic to form the second series,and answer the question given below the second series. See the following example.

Example No. 1: In the following question a series is given and it is followed by the starting point of another series. After this, a question is given, you have to complete the second series by applying the same logic as in the first given series, and then you have to answer the question.

5 8 12 17 23 30

9 a b c d e

Which number should come in place of c?

Solution:In this question, it canbe analyzed that the difference between the numbers is 3, 4, 5, 6 and 7. So youhave to apply the same logic and start the series with 9. The first numberafter 9 would be 9 + 3 = 12 (this would replace letter a), the second numberwould be 12 + 4 = 16 (this would replace letter b) and the third number wouldbe 16 + 5 = 21 (this would replace the letter c). You need not to go furtherbecause the question is related to c only.

Example No. 2: In the following question, a series isgiven and it is followed by the starting point of another series. After this aquestion is given, you have to complete the second series by applying the samelogic as in the first given series, and then you have to answer the question.

8 9 13 22 38 63

12 a b c d e

Which number should come in place of d?

Solution:In this question, the squares of the natural numbers are added. Firstly 1 is added, then 4, then 9and so on. You have to apply the same logic and add 1, 4, 9 and 16 to get the value of d. After adding 1, you’ll get 13 which is the value of a, then after adding 4 you’ll get 17, which is the value of b, after an addition of 9 you’ll get 26 which is the value of c.After this add 16 and get 42, which is the value of d.

Example No. 3: In the following question, a series isgiven and it is followed by the starting point of another series. After this a question is given, you have to complete the second series by applying the same logic as in the first given series, and then you have to answer the question.

2 3 5 7 11 13

23 a b c d e

Which number should come in place of b?

Solution: In this case, it can be seen that the series is of prime numbers. As the second series is starting from23, the next prime number is 29 (which is at the place of a), thereafter the next prime number is 31 (which would be at the place of b) and is the right answer.

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Some other common types of number series involve the following types of logic:

1.Prime Numbers: EXAMPLE : 3,5, 7, 11, 13, 17, ? (19)

2.Successive Addition, Deletion, Multiplication etc.

EXAMPLE: 4, 6, 10, 16, 24, 34, …?...60 Add +2, +4, +6, +8, +10, … (46)

3. Adding different numbers at regular intervals:

EXAMPLE: 17, 23, 29, 35, ….?….., 47 Adding 6 each time (41)

EXAMPLE: 8, 23, 44,……,104, 143 Adding 15, 21, 27, etc. having a fixed gapof 6 each (71)

4.Adding/ deleting prime/odd/even numbers in the preceding terms:

EXAMPLE : 1,2, 5, 10, 17, …?….37 Adding odd numbers 1, 3, 5, 7, 9 (26)

5.Terms regularly multiplied/divided by natural/odd/even numbers

EXAMPLE:

Thenext number, as is clear from the above illustration, should be 480 x 6=2880

6.Square/Cube of a number Plus/Minus any natural number

EXAMPLE: 2,10, 30, 68, …?…, 222 1³+ 1, 2³+ 2, 3³+ 3, 4³+ 4….. (130)

EXAMPLE:0, 2, 6, 12, …?…., 30 1²- 1, 2²- 2, 3²- 3, 4²- 4, 5²-5…. (20)

Sometimes a double series combining numbers and letters may also be given. The logic involved in such cases is also the same as we have discussed earlier. Questions on wrong or misfit number in the series involve the same kind of logic which we have discussed before.

Look at this one:

We have to find the number which is a misfit in the series. As illustrated above, the last number in the series should have been 6240, which is not there. Therefore, 6250 is the correct answer.

Number Series: 10 Solved Examples

noreply@blogger.com (Anonymous) — Tue, 22 Nov 2011 05:26:00 +0000

Example No. 1: 17, 23, 29, 35, ?, 47

Solution:In this case, 6 has been added to all the numbers to generate the next number. Firstly 17 + 6 = 23, then 23 + 6 = 29 and so on. In order to get the next number after 35, 6 would bea dded in that. Therefore, the question mark should be replaced by 35 + 6 = 41.

Example No. 2: 1, 2, 5, 10, 17, 26, ?

Solution: In this example, the odd numbers have been added in the increasing order. Firstly 1, then 3, then 5and 9 in the end. Then, in order to obtain the next number, 11 should be added.Therefore, the next number would be 26 + 11 = 37.

Example No. 3: 4, 4, 8, 24, 96, 480, ?

Solution: In this question,every number is multiplied by the next natural number starting with 1. You can understand this from the following diagram.

The next number, as is clear from the above illustration, would be obtained by multiplying the last number 480 by 6. So the answer is 480 * 6 = 2880

Example No. 4: 2, 10, 30, 68, ?, 222

Solution:In this question, the method of adding the same/different number in the perfect cubes of the natural numbers, is applied. Here in this case, the cube of a natural number is added to the number. I.e. these numbers are 1³+ 1, 2³+ 2, 3³+ 3, 4³+ 4, and the answer would be 5³ + 5 Þ 130.

Example No. 5: 0, 2, 6, 12, ?, 30

Solution:In this question, from the square of a natural number, the same number has been subtracted. The numbers are obtained as 1²- 1, 2²- 2, 3²-3, 4²– 4. Therefore the next number would be 5² – 5 =20.

* Double Series:Much more common in tests are questions on double number series. In such questions, two series are mixed up alternately. Have a look at the following example.

Example No. 6: 5, 5, 15, 7, 45, 11, 135, 13, 405, ?

Solution: In this question two series run concurrently. Whenever two series are going on, naturally, every alternate term would be belonging to the other series. You may analyze this from the following diagram.

It can be seen clearly that one series out of these is of prime numbers while the other series is number multiplied by 3. Apparently, the missing number belongs to the category of prime numbers, so the next prime number after 13 is 17 and is the right answer.

Example No. 7: 6 6.5 7.5 9 11 13.5 ?

Solution:In this question, the addition factor is increasing continuously by 0.5. The first addition done is 0.5,the second is 1, the third is 1.5 and so on. In the last the addition to be done is 2.5 + 0.5 = 3. So the answer would become 13.5 + 3 = 16.5.

Example No. 8: 4 9 17 35 69 139 ?

Solution:In this question, the logic applied is ´ 2 + 1 and ´ 2 – 1 alternately. In the end what is done is ´ 2 + 1 and in order to get the next term ´ 2 – 1 is to be done. So the answer would be 139 ´ 2 – 1 = 277.

Example No. 9: 2 2 3 6 15 45 ?

Solution:In this question, the multiplier increases by 0.5 each time. Firstly multiplied by 1, then by 1.5,then by 2, then by 2.5 and so on. In the question the second last given number has been multiplied by 3 to get the last number. Now in order to obtain the next number, we should multiply the last number by 3.5. Then answer would be 45´ 3.5 = 157.5.

Example No. 10: 23, 35, 57, 711, 1113, ?

Solution:In this question, the logic is very simple. Two consecutive prime numbers have been combined and represented as a single number i.e. 2 and 3 Þ, then 3 and 5 Þ 35, then 5 and 7 Þ 57 and so on. Every number starts with the same prime number with which the last prime number ended. The next prime numbers to betaken are 13 and 17 and the number would be 1317.

Number Series

noreply@blogger.com (Anonymous) — Sun, 20 Nov 2011 10:18:00 +0000

Questions based on number series are a favourite with most examiners. In such a question, if it consists of a single series of numbers, they are arranged in a particular manner and each number is related to the earlier and the following numbers in a particular way. The examinee is supposed to decode the logic involved in the sequence and then fill in the space containing the question mark with a suitable choice out of those given. But before we proceed to discuss the various types of questions related to them, we will talk of some basic facts which are essential to an understanding of these types of questions.

Consider the following example, which can be labelled as one of the easiest one can think of.

Quite often, you can find the right answer in number series by taking the difference between consecutive pairs of numbers, which form a logical series. As in the above example, the differences between succeeding pairs of numbers are 3, 5, 7,9, 11, 13. Logically speaking, the next difference must be 15. This 15, if added to the last number 49, gives you 64, which is the correct answer. But thinking from a different viewpoint, all these numbers given in the questions are squares of natural numbers 1, 2, 3, 4, 5, 6, 7. So the next number in the series should be the square of 8, which is 64. So we can get the same correct answer in series, even if we adopt two different logical approaches.

An important conclusion emerges from this example, i.e., if we remember squares upto a reasonable limit, say 32 and cubes upto 30, we can get a lot of help in solving such questions. Decoding the logic in a series becomes quite easy, if one has an idea of different squares and cubes. Overall, finding the differences between two consecutive numbers or two alternate numbers (if there are two parallel series running) remains the most helpful approach to solving such questions.

Now examine the following series:

The above series involves two operations, multiplication and addition of a number by the same number. The series runs like this 1x1+1=2, 2x2+2=6, 6x3+3=21,21x4+4=88, 88x5+5=445. The next number, following this logic, should be445x6+6=2676. This is one case where the idea of differences will not help us.

Many number series are based on squares, cubes and addition/subtractions to/from them. Have a look at the following case.

EXAMPLE

Obviously,the first differences do not appear to contain any logic. But if we take the differences among differences as illustrated above, the logic becomes clear. By the same logic, the last addition to the last number i.e. 30, should be 6,which makes it 36. Moving backwards, 36+90+210=336, which is the correct answer. But this method proves to be time-consuming.

Adopting a more sophisticated approach, these numbers move in this fashion.

1³- 1, 2³ - 2, 3³- 3, 4³- 4, 5³- 5, 6³- 6. Following the same logic, the next number in the series has to be 7³- 7 =336.

Example No. 4: 3,5, 7, 11, 13, 17, ?

Solution: This is a series of prime numbers, it can be clearly seen that every number given isprime in the same numerical order. The next prime number would be 23, the right answer.

Example No. 5: 4, 6, 10, 16, 24, 34, ?, 60

Solution:In this case the addition to the numbers increases by 2 i.e. first 2 is added, then 4, then 6and so on. It can be seen that before the questions mark 10 has been added,therefore, the next addition would be 12. And the number would be 34 + 12 = 46.

Logical Consistency

noreply@blogger.com (Anonymous) — Sat, 19 Nov 2011 12:32:00 +0000

In logical consistency questions, you are given a main statement followed by four statements. You would have to pick a combination of two of these four statements, which are logically correct and are consistent with the main statement given. Consider the following example:

R is in the room when P is in the hotel.

Can R be in the room when P is not in the hotel?

YES

The condition given in the first statement is that if P is in the hotel then R definitely has to be in the room.

R can be in the room otherwise also i.e. when P is not in the hotel.

The valid conclusions you can make about the main statement given are:
(a) P is in the hotel; R is in the room (straight logic)

(b) R is not in the room, P is not in the hotel (straight negation)

The statement above is also correct because, at any given point of time R and P have two possible positions each i.e. R can be in the room or outside.

P can be in the hotel or outside

When R is not in the room; P has two options, of either being in the hotel or outside. However it can be said definitely that P is not in the hotel because if P is in the hotel than R would be in the room, but R is outside, so P has to be outside. There are some standard types of questions in this category.

I. If type

II. Either – or type

III. Whenever – type

IV. May-be type

A simple logical can be followed in all these questions. Every main statement will have two parts X and Y. For example in the statement

R is in the room, when P is in the hotel.

X is ‘P is in the hotel’.

Y is ‘R is in the room’.

If the condition is when X then Y the valid conclusion would be when not Y then not x.
If X happens then Y will Happen

Now if Y happened it does not necessarily mean that X has also happened. Keep this point in mind and the exercises will be easy.

Coding Decoding 15 Solved Examples # 2

noreply@blogger.com (Anonymous) — Fri, 18 Nov 2011 11:52:00 +0000

Example No. 1: If HARISH is coded as ITJSBI, then how would REEMAbe coded?

Sol: In this case, the immediate next letter in the alphabet is taken and the code is written in the reverse order i.e. the code for the letter H is I and it is in the end, the code for A is B and it is second from the end, similarly the code for R is S and it is third from the end and so on. While coding the word REEMA, the code for R will be S and it would be written in the end, similarly the codes for E, E, M and A would be F, F, N and B respectively. And the final code would be BNFFS. This type is called as+1 and reverse order.

Example No. 2: If CALENDAR = QZCMDKZB, then NEELAM = ?

Sol: This type is just a bit different from the previous type. This is called – 1 and reverse order. Now C – 1 = B and it is the last letter in the code, code for A, L, E are Z, K and D respectively and these are written as the second, third and fourth letter respectively from the end of the word in the code. Similarly the code for the word NEELAM would be LZKDDM.

Example No. 3: If RELATION = 95312965, then MANAGEMENT = ?

Sol: In this case, the code for every letter is its position in the alphabetic order, represented as a single digit. If its position is already a single number, then it is simply assigned as the code,and if there are two digits in its position, then those digits are added to get the code for that letter. In this case R is the 18^th letter so itscode would be 1 + 8 = 9, E is the 5^th letter so its code is 5, L isthe 12^th letter so its code is 1 + 2 = 3, A is 1 and so on.Similarly when the code for the word MANAGEMENT is made. M is 13, 1 + 3 = 4. A= 1, N is 14 1 + 4 = 5, A = 1, G = 7 and so on. The final code for the word MANAGEMENT would be 4151754552

Example No. 4: If the code for the number 84219643 is 24139864,then what is the code for 97658256 ?

Sol: In this case, the eight-lettered number has been broken into two parts i.e. 84219643, the underlined part is 1st part starting with 2 and ending with 6,the second part is 4384, starting with 4 and ending with 4. So while making code 1 number from each part is taken. 2 is taken from part 1, then 4 is taken from part 2, 1 is taken from part 1, 3 is taken from part 2 and so on.

Similarly while coding 97658256, you should also take the digits at the same position as the first part i.e. 6582 and the second part would be 5697. 6 will be taken from 1st part, 5 will be taken from2nd part, 5 would be taken from the first part, 6 from the second part, 8 from the 1st part, 9 from the second part, 2 from the first part and 7 from the second part. So the code is 65568927.

Example No. 5: If SHIVANI = 574, then GANESH = ?

Sol: in this case, EJOTY of all the words has been added,multiplied by the number of letters in that word. SHIVANI => S = 19, H = 8, I = 9, V = 22, A = 1, N = 14, I = 9 => 19 + 8 + 9 + 22 + 1 + 14 + 9 = 82 × 7 ( .: there are 7 letters in the word SHIVANI), Similarly while making code for GANESH => 7 + 1+ 14 + 5 + 19 + 8 = 54 × 6 ( .: there are six letters) = 324 would be the code.

Example No. 6: If ACTIVITY = 24315137, Then ELEPHANT = ?

Sol: It involves the position of alphabet in the alphabetic order + 1. If it becomes a single digit number, write it and if it is a two digit number then add it to get a single digit number as in question no. 13. Similarly ELEPHANT => E = 5 + 1 = 6, L = 12 +1 = 13 => 1 + 3 = 4, E = 5 + 1 =6, P = 16 + 1 = 17 => 1 + 7 = 8 and so on. The code will become 64689263.

Example No. 7: If EVITCDNIV = HZNZJLWSG, then ABDICTION = ?

Sol: In this question, firstly + 2, then + 3, +4, +5, +6,+7 and so on. Similarly when the code for the word ABDICTION is made firstly+2, then +3, +4, +5, + 6 and so on. The code will finally become DFIOJBNYY.

Example No. 8: If PERSON = THTWRP, then ENGINE = ?

Sol: Here P + 4 = T, E + 3 = H, R + 2 = T, Then S + 4 =W, O + 3 = R, N + 2 = R. The method for coding is +4, +3, +2. The code forENGINE will become E + 4 = I, N + 3 = Q, G + 2 = I, I + 4 = M, N + 3= Q and E +2 = G. Therefore the code is IQIMQG.

Example No. 9: If SILVER = HROEVI, then MEENAKSHI = ?

Sol : In this case, if the letter is at ‘nth’ position from the beginning then the letter at ‘nth’ position from the end is written. This can always be checked, whenever the sum of the number and its respective code is 27. Then the method applied for the coding would be this only. As in SILVER, S is 19 and its code H is 8 and the sum is 27. I is 9 and its code R is 18 and sum is 27. While coding MEENAKSHI, the same method coding will be applied. M is 13, so what should be added in 13 to make it 27 ( that is14), write the 14^th letter which is N as the code for M. Similarly E is 5, find 22^nd letter to make sum as 27 ( V is 22^ndletter) and that is the code and so on. The code for the word MEENAKSHI will be NVVMZPSR.

Example No. 10: If A = E, B = F, C = G and H = L, how will the word COME BACK be coded in this code?

Sol : Here in this case, it can be checked that 4^thletter has been made the code for every letter, in the same way, you can the 4^thletter as the code for every letter i.e. COME BACK would become as C + 4 = G, O will be S and the code would become – GSQI FEGO.

* Sometimes the complete pattern of numbers/letters codes are given for coding and based upon that you have to code the words/numbers.

Example No. 11: The questions given below are based upon the following set of codes.

Digit : 1 0 6 4 2 9 8 7 5

Code : M O X L S T N H P

A) Find the code for 24750.

1.SLPHO 2. SHLPO 3. SLOPH 4. SLHPO

B)Find the code for 814005

1.NMLOOH 2.NMLPPO 3. NMLOOP 4.NLMOOP

Now here in this case, it can be verified that the code for the 2 is S, 4 is L, 7 is H, 5 is P and 0 is O.Therefore the code in the first case would become SLHPO and in the second case the code would be NMLOOP.

Example No. 12: In a certain code. ‘sim ma kom’ means ‘bring me water’. ‘ma mo mok’ means ‘water is life’. ‘jka od sim’ means ‘give me toy’ and ‘mo min not’ means ‘life and death’. Which of the following is representing ‘is’ in that language?

1.mo 2. ma 3.mok 4. min

Sol: Here in such questions by combining two groups, the code for one particular word can be decided.

In the first two coded sentences, the only code common is ‘ma’ and the only word common is ‘water’. This implies that ‘ma’ is the code for ‘water’. Similarly in the second and fourth coded sentences the only code common is ‘mo’ and the only word common is ‘life’. This implies that the code for the word ‘life’ is ‘ma’.After this in the second coded sentence the only code remaining is ‘mok’ and the only word remaining is ‘is’, So the code for the word ‘is’ is ‘mok’.

Example No. 13 : In a certain code, ‘952’ means ‘order my tape’ ‘849’ means ‘buy great tape’ and ‘246’means ‘buy my water’. Which of the following digits represents ‘great’ in that code?

1.2 2. 6 3.8 4. 5

Sol: Here by comparing sentence 1 and 2 get the code for the word ‘tape’ which is 9. By comparing second and third sentence get the code for the word ‘buy’, which is 4. So the remaining word in the second sentence is ‘great’ and the remaining code is 8. So the answer is 8 which is the third option.

Sometimes the coding is done in groups, i.e. only if the complete block can be decoded only then the questions can be answered. Look at the following example.

Example No. 14:

i.What is the code for G?

ii.What is the code for H?

iii.What is the code for S?

iv.What is the code for R?

Sol: In such cases, to every particular letter, the code assigned is the same. By combining two or three words, the code for 1 or 2letters can be decided. It will be solved like, in the word ‘HELLO’, there are two L’s and in the code there are two D’s. So the code for letter L is D. In the word GEORGE, there are two G’s and two E’s & in the code there are two F’s and Y’s so either of F and Y is the code for G. After this, take the word GUMS, in which there is G but not Y and code out of F and Y is only F. So F is the code for G. Similarly by comparing RAGS and HERO the code for R is O can be decided, because the only letter common is R and the only code common is O. Now when you have got the code for G, you can take the words GUMS and RAGS, in which besides G, S is also common and the second code common (besides F) is N.So N is the code for S and so on, the code for all the letters needed can be found out.

Sometimes a very different type of question is asked. In the directions four/five types of coding methods are given, then from the question itself you have to recognize which type of coding is done.

Example No. 15: Given below are five possible ways of coding a word. Study carefully and report which of the methods has been used in each case.

1. GRAPES is coded as TFQBSH

2. APPLE is coded as DSSOH

3. ORANGE is coded as LOXKDB

4. COCONUT is coded as OCOCUNT

5. PINEAPPLE is coded as ELPPAENIP

A. COMPUTER is coded as OCPMTURE.

1.1 2. 2 3.3 4. 4

In this question, it can be seen, that simply the code is made by interchanging the pairs of letters as in the case of4^th type. CO was made as OC, then again CO as OC, then NU as UN andt he last letter was alone, so it was just left. So the answer to this question is the 4^th type of code, which is given as potion no. 4.

B. FLOPPY is coded as IORSSB.

1.5 2. 3 3.2 4. 1

In this question, the coding done is +3, i.e. every letter is replaced by a letter which is after three places in the alphabet, which is the case in the second type of coding. So second type of coding, which is given in option no. 3, is the answer.

C. GLOBALISATION is coded as OPJUBTJMBCPMH.

1.4 2. 3 3.2 4. 1

In this case, the coding done is +1 and writing it in the reverse order i.e. as in first type of coding replacing everyl etter with its next =letter in the alphabetic order and then writing the code in the reverse order (the code for the first letter is written at the last position, the code of the second letter is written in the second last position and the code of the last letter is written at the first position).

D. IMBECILE is coded as LPEHFLOH.

1. 4 2. 3 3.5 4. 2

Coding Decoding Solved Examples # 1

noreply@blogger.com (Anonymous) — Thu, 17 Nov 2011 18:49:00 +0000

Example No. 1: If the word MAHESH is written as PDKHVK, then how will the word SEEMA be written in that code?

Sol: In this case three has been added in each of the letters in the word. This can be stated as that the third letter has been taken for each of the letters, i.e. two letters are left in the letter and its code.Therefore while coding SEEMA, add 3 in S and get V, similarly add 3 in E and get H, add 3 in E and get H, add 3 in M and get P and in the end add 3 in A and get D. The code for the word SEEMA will be VHHPD.

Example No. 2: If the word AMITABH is coded as HBATIMA, then how will you code the word ANUPAM?

Sol : In this the whole of the word is written in the reverse order only, then the word ANUPAM would also be written in the reverse order and MAPUNA would be obtained as answer.

Example No. 3: If HEMA => EHAM, Then REKHA = ?

Sol: In this one, the pairs of letters are interchanged,similarly the pairs in the word REKHA would be interchanged. And ERHKA, because A is the only letter that remains, and it would be written as it is.

Example No. 4: If the word RADHA is coded as QZCGZ, then how will you code the word PARVATI ?

Sol: In this case, -1 is done i.e. the previous letter of each of these alphabets is taken. Similarly while coding PARVATI, we will subtract 1 from each of the letters => P – 1 = O, A – 1 = Z, R – 1 = Q, V – 1 = U, A – 1 =Z, T – 1 = S and I – 1 = H, the code will be OZQUZSH.

Example No. 5: If the word RAMESH is written as 181135198, how willyou write the word SUNITA?

Sol: Now in this case, simply the position of the alphabet is written i.e. R = 18, A = 1, M = 13 and so on. Similarly while making code for the word SUNITA, their alphabetical positions will be written i.e. S = 19, U = 21, N = 14, I = 9 and the

code will become 1921149201

Example No. 6: If RAM => 32, then SHAM = ?

Sol: In this question, the code for the word RAM has been made by adding the positions of all the alphabets in the word i.e. R = 18, A =1, M = 13 Þ 18 + 1+ 13 = 32.Similarly when the code for the word SHAM would be made, it will be S = 19, H =8, A = 1 and M = 13 Þ 19 + 8 + 1 + 13 = 41.

Example No. 7: If ABHISHEK => BAIHTGFJ, then HRITIK = ?

Sol: In this case, both +1 & - 1 are applied. A + 1 =B, B – 1 = A, H + 1 = I, I – 1 = H, S + 1 = T, H – 1 = G, E + 1 = F and K – 1 =J, Similarly the code for the word HRITIK will be made i.e. H + 1 = I, R – 1 =Q and so on. The code will be IQJSJJ.

Example No. 8: In a certain code the word ADARSH is written as ZOZXYP, how would RADHA be written in the same code?

Sol: Now in this case, the coding done cannot be cracked easily. The simple method which is to be applied in this case is that all the letters of the word RADHA are present in the word ADARSH, so corresponding codefor each letter would be taken. Firstly take code for R i.e. = X, then take code for A i.e. = Z. Similarly taking the codes for other letters, the word RADHA would be coded as XZOPZ.

Example No. 9: If RAM =9, SUDHA = 25, RAMESH = ?

Sol: Now the logic applied here is very simple. There are3 letters in the word RAM, so its code is 3² = 9, similarly there are 5 letters in the word SUDHA, so 5² = 25. As there are 6 letters in the word RAMESH, so its code will be 6² = 36.

Example No. 10: If RAMESH = AEHMRS, then ANURADHA = ?

Sol: In this case, the coding is simply done in the increasing position of alphabets i.e. the dictionary order.

i.e.arrange the alphabets in the same order as they are in the actual alphabetic order. Firstly A comes, then E, then H, then M, R and S respectively. Similarly when the code for the word ANURADHA is made, it would be like AAADHNRU.

Understanding Coding-Decoding

noreply@blogger.com (Anonymous) — Thu, 17 Nov 2011 18:41:00 +0000

Coding questions are very popular with most examiners. There is so much of variety in these questions, that one know 30 – 40 types of coding in order to attempt these questions in the examination.While framing coding questions, the examiner tries to include one or two very new types of coding in the examination. In order to gain proficiency in this topic, besides reading and understanding all the questions, try to frame 20 –30 questions on this theme and ask one of your friends to do the same. Then first attempt the questions made by your friend and simultaneously, let him solve the questions made by you. Then by sitting together discuss all the questions. This is a very useful technique to gain mastery on this topic.

In such a question, generally, a word and its code are given and the students are asked to find the code for the other given word, applying the same logic, as what has been applied in the given examples.

But before we proceed to discuss the various types of questions related to coding,it is better to have an idea regarding the general types of coding. Some of the major types of coding are:

1. Constant addition in the position of alphabets.
2. Constant subtraction in the position of alphabets.
3. Denoting the position of alphabets in the whole alphabetical order.
4. Addition of the positions of all the alphabets to make code for the word.
5. Constant addition and subtraction respectively in the position of all the alphabets.
6. Squaring the number of letters in the word.
7. Arranging the letters in the alphabetic order.
8. Arranging the letters given in the main word, in the reverse order.
9. Interchanging each pair of the letters, in the whole word.
10. Constant addition and then reversing the letters to make the final code.

Now we will discuss all these types of coding and much more with the help of examples.

You must have noticed from the above points, that it is very important for the student to know the order of all the alphabets.

The following method can be applied to learn the alphabetic order.

I.THE ALPHABET: The normal English alphabet contains 26 letters in all, as shown above

(Usually,questions on alphabet are accompanied by this normal alphabet). From A to M,the alphabet completes its first half, while the other half starts from N and ends at Z.

A-M - 1-13 (First Alphabetical Half )
N-Z –14-26 (Second Alphabetical Half)

II.EJOTY: For purpose of convenience, it is helpful to remember this simple formula called EJOTY, with the help of which you can easily find the position of any letter without much effort. But for practical purposes, you should learn by heart the positions of different letters in the alphabet, where these five letters represent the following positions.

E J O T Y
5 10 15 20 25

Important Relationships which are repeatedly asked in the examination

noreply@blogger.com (Anonymous) — Wed, 16 Nov 2011 18:42:00 +0000

The son of my father : Myself or my brother
Mother’s or Father’s son : Brother
Mother‘s or Father’s daughter : Sister
The only brother of my father’s son : Myself or my brother
Mother’s brother : Maternal uncle
Father’s brother : Uncle
Mother’s sister : Maternal aunt
Father’s sister : Aunt
Mother’s mother : Maternal Grandmother
Father’s mother : Grandmother
Mother’s father : Grandfather

Father’s father : Grandfather
Son’s wife : Daughter – in –law
Daughter’s husband : Son– in – law
Husband’s or wife’s sister : Sister-in-law
Husband’s or wife’s brother : Brother-in-law
Brother’s son : Nephew
Brother’s daughter : Niece
Uncle or aunt’s son or daughter :Cousin
Sister’s husband : Brother-in-law
Brother’s wife : Sister-in-law
Grandfather’s only son : Father
Grandmother’s only son : Father
Grandfather’s son : Father or uncle
Grandmother’s son : Father or uncle
Grandfather’s only daughter-in-law :Mother
Grandmother’s only daughter-in-law :Mother

Blood Relations

noreply@blogger.com (Anonymous) — Wed, 16 Nov 2011 18:27:00 +0000

This type of problems involves an analysis of certain blood relations and then deriving inferences on the basis of the given information. Some examples of such questions are as follows.

a) Anupam said to Kapil, “That girl playing with hockey is the younger of the two sisters of the son of my father’s wife”. How is the girl playing hockey related to Anupam?

b) Sudha sees a photograph and points at a man in the photograph and says, “His brother’s father is the only son of my grandfather”. How is Sudha related to the man in the photograph?

In such questions the examiners generally try to assess the aptitude of the examinee regarding analyzing various relationships. Since in this case, generally the questions are to be solved by analyzing and visualizing the relationships, it is very much helpful in gauging the examinee’s visualization in a limited time. The best possible technique to solve such questions has been given in the coming pages. If you are not able to decide the relationship, put yourself in the question (in the place of the person who is making the statement) and then try to find the answer.

Backtracking means starting with the last information and proceeding backwards. For example, if it is given that he is the son of the mother of my grandfather’s daughter, then we proceed with the last information:‘grandfather’s daughter’. Grandfather’s daughter means aunt (sister of father).Now ‘mother of my grandfather’s daughter’ becomes ‘mother of my aunt’. Mother of my aunt is my grandmother. Hence, he is the son of the mother of my grandfather’s daughter becomes ‘son of my grandmother’, which is father or uncle.

Asin the above given question a) Anupam says to Kapil, ‘my father’s wife’, meansmother, her son (either yourself or your brother, his two sisters (means yoursisters), so the girl playing with hockey is Anupam’s sister.

b)Sudha says in the end, only son of my grandfather which means father only, heis the father of a man’s brother means father of Sudha’s brother. So Sudha issister of the man in the photograph.

Letus have some more examples to gain clarity about this idea.

Example No. 1: Pointing to aphotograph, Rajesh said, “she is the mother of my mother’s mother’s daughter”.How is Rajesh related to the woman in the photograph?

Solution: My mother’s mother’sdaughter means either my mother or my mother’s sister. Mother of my mother ormy mother’s sister means my maternal grandmother. Therefore the man is thematernal grandson of the woman in the photograph.

Example No. 2: Pointing to a boy inthe photograph, Minakshi said, “His sister is the only daughter of my father”.How is the boy related to Minakshi’s father?

Solution: My father’s onlydaughter means Minakshi herself. She is the sister of the boy in the photograph.This means the boy is the brother of Minakshi. Therefore he is the son ofMinakshi’s father.

Example No. 3: Introducing Madhuri,Anil said, “She is the wife of my mother’s only son”. How is Madhuri related toAnil?

Solution: My mother’s only sonmeans Anil himself. Now Madhuri is the wife of that person, means she is thewife of Anil.

Example No. 4: Pointing to Kajol,Ajay said, “Her mother’s only daughter is my mother”. How is Ajay related toKajol?

Solution: Here in this statementAjay’s mother is the only daughter of his maternal grandmother.

Hismaternal grandmother is the mother of Kajol (because Ajay points to Kajol andsays her mother - means Kajol is Ajay’s mother.

Example No. 5: Rahul said to Raveena,“Your only brother’s sister is my mother”. How Raveena is related to Rahul’smaternal grandmother?

Solution: Here the statementends with my mother, means Rahul’s mother and she is the sister of Rahul’smaternal uncle (mama) and he is the only brother of Raveena, means eitherRaveena is Rahul’s mother or maternal aunt (maasi).Now the question is how Raveena is related to Rahul’s maternal grandmother. Itcan be clearly identified that she is the daughter of Rahul’s maternalgrandmother.

Note: Unless otherwise mentioned, all blood relationsare to be taken from the paternal (father’s) point of view i.e. if grandfatherhas been mentioned it would be taken as father’s father and not as mother’sfather unless maternal grandfather is mentioned.

Thistechnique of backtracking is applied in such questions where a single statementis given. But sometimes there are questions in which the information isprovided in the form of points. Then it is advisable to arrange the informationin the form of a family tree.

The following rules can be kept inmind, to solve the questions relating to relation in an easy way.

a) Verticalor diagonal lines should be used to represent parent-child relationships i.e.if the generations are different, these should be represented vertically.

b) Ifthe relationship is of the same generation, it should be representedhorizontally.

c) Asingle arrow should be used to mark a relationship of brother or sister i.e.

d) Adouble horizontal line (like Û) should be used to represent marriages.

e) Puta + sign before someone who is a male and a – sign before someone who is afemale.

f) Wheneversomething is not known put a ? mark or some such symbol before it.

Here is an illustration:

Theabove example tells us that:

(i) Y and Z are a couple; Yis the husband while Z is the wife.

(ii) Y has a sister X.

(iii) The couple, Y and Z, hasthree children: T, P and another son, whose name is not known. P is also sonwhile the sex of T is not known.

(iv) T and the other unknownson are unmarried while P is married to Q.

(v) The couple, P & Q,has a daughter J and a son whose name is not known.

Given the process, how to solve such questionsquickly?

1. Read the informationgiven quickly, it will give you the idea of the problem.

2. Use the actualinformation given to make a family tree. It is better to start from therelation of a single degree i.e. no third person is involved in that. Therelation should be a direct one, instead of taking uncle and nephew, it isbetter to take father and son or brother and sister.

3. When you start making thetree, try to attach the further information given to the tree already madeonly.

4. Then combined all theinformation and answer the questions accordingly.

Example No. 6: P is brother of Q, R is sister of Q. How P isrelated to R?

Solution:

Itcan be clearly seen that P is the brother of R.

Example No. 7: X and Y are brothers.C and D are sisters. A’s son is D’s brother. How is Y related to C?

Solution: It has been clearlyindicated that Y is the brother of X, X’s son is D’s brother. This implies thatD is the daughter of X. Since C and D are sisters, C is also the daughter of X.So Y is the uncle of C.

Example No. 8: M and N are a marriedcouple. O and P are brothers. O is the brother of M. How is P related to N?

Solution: Mand N are husband and wife. Since O and P are brothers, and O is the brother ofM, P is also the brother of M. Thus, P is the brother-in-law of N.

Example No. 9: A family consists of 5members P, Q, R, S and T. The last one (T) has two sons, an unmarried daughterand a daughter in law. P is the brother-in-law of the above mentioneddaughter-in-law. Q’s sister is not happy with Q’s wife. But P and his fathersupport Q’s wife ‘S’. Who is the daughter of T?

Solution: In this question, ithas been clearly mentioned that T is having 2 sons, 1 daughter and a daughterin law. Now if P is the brother in law of the daughter-in-law of T means P isthe son of T. Secondly if Q’s sister is not happy with Q’s wife implies theother son of T is Q and lastly it has been mentioned that Q’s wife is S. So theonly remaining character is T’s daughter and the only remaining name is R. ThusR is the daughter of T.

Example No. 9(a): What is the relationof P with S?

Solution: Now it has already beenseen that P is the unmarried son of T and S is the daughter-in-law of T. So Pis the brother-in-law of S.

Example No. 9 (b): How is T related to Q?

Solution: It has already been decidedthat T is father of Q.

Example No. 9 {c} : Who is the wife of Q?

Solution: It is clear that thewife of Q is S.

Example No. 10: A is brother of B, Cis the father of A, D is a brother of E, E is a daughter of B. Who is the uncleof D?

Solution:

It can be seen from the diagram that theuncle of D is A.

Data Sufficiency

noreply@blogger.com (Anonymous) — Tue, 15 Nov 2011 06:58:00 +0000

What is Data Sufficiency

As the name suggest, Data Sufficiency is a typical set of problems asked not only in CAT but in other national and international exams. The conceptual knowledge and skills required to solve Data Sufficiency problems are far easier than that required to solve standard Problem Solving questions. Fundamental knowledge of the principles of arithmetic, algebra and geometry is sufficient. Then why these questions exist??? The data sufficiency questions are designed to test our reasoning and logical ability, more than the mathematical skills.

i.e. If someone asks what is 2x+11. We can’t tell as we do not know the value of x.

Now, someone tells us that x is a positive integer <2.

Can you tell now? Yes

Yes because x is now 1 and 2x +11=13.

General Pattern of Data Sufficiency Problems:

A Data Sufficiency problem consists of a mathematical or logical problem followed by two statements containing information relating to it. The students must decide whether the problem can be solved by using the information from the given statement combined or individually. Choose your answer as 1, 2, 3 or 4 as per the directions given below.

Directions: Each question is followed by two statements, I and II. Answer each question using the following instructions:

Choose 1: if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2: if the question can be answered by using either of the statements alone.
Choose 3: if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 4: if the question cannot be answered even by using both statements together.
In Recent Past, with five options given in most of the exams, options 1 have been broken into two parts.

Now the options look like

Choose 1 if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2 if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3 if the question can be answered by using either of the statements alone.
Choose 4 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5 if the question cannot be answered even by using both statements together.

Let us see some examples to understand the above in depth.

[Solved Example]

Example 1:
Directions: The question below is followed by two statements, I and II. Answer each question using the following instructions:
Choose 1 if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 4 if the question cannot be answered even by using both statements together.

Question : Is x-y positive?
Statement 1: x is a natural number
Statement 2: y is negative integer

Solution:
Statement 1 tells us that x is a natural number but doesn’t tell us anything about y so you can’t say about x-y.
Statement 2 tells that y is a negative integer but doesn’t tell you anything about x so you can’t say about x-y.

Now, to check for option 3, we can combine the information from both statements. x is a natural number so x=1,2,3,4-------- whereas y=-1,-2,-3-------

And x-y would always be positive so you can tell x-y is always positive with confidence. Hence Choose 3.

[Points to Remember]
Under time constraints, while analyzing the statements a student normally makes the mistake of carrying over information from one statement to another. Remember data sufficiency is designed to test your patience. You should not jump to a conclusion or make any assumption regarding data. You only know what is written in the question. So while analyzing statement 2 alone, you have to assume that you haven’t read Statement 1 yet.

[/Points to Remember]

Now, let us use the same example with only one variation.

[Solved Example]

Example 2:
Directions: The question below is followed by two statements, I and II. Answer each question using the following instructions:
Choose 1 if the question can be answered by using one of the statements alone,but cannot be answered using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 4 if the question cannot be answered even by using both statements together.

Question: is x-y positive?
Statement 1: x is a negative integer.
Statement 2: y is a natural number.

Solution:
Statement 1 tells us that x is a negative integer but doesn’t tell us anything about y so you can’t say about x-y.
Statement 2 tells that y is a natural number but doesn’t tell you anything about x so you can’t say about x-y.

Now, to check for option 3, we can combine the information from both statements. x is a negative integer so x=-1,-2,-3------- where as y=1,2,3,4------

And x-y would always be negative so you can tell x-y is always negative with confidence.

So which option should you choose? Students make mistake here by choosing 4 because you think x-y should be positive. No, the question is

Is x-y positive and the examiner is looking for a definite answer. In Example 1, it was ‘Yes’ and in Example 2 it is ‘No’. So ‘No’ is also an answer and hence option 3 is right answer even in Example 2.

Now, let us modify the above problem to see a different variation.
[Solved Example]

Example 3:
Directions: The question below is followed by two statements, I and II. Answer each question using the following instructions:
Choose 1 if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 4 if the question cannot be answered even by using both statements together.

Question: Is x-y positive?
Statement 1: x is a integer.
Statement 2: y is a natural number.

Statement 1 tells us that x is an integer but doesn’t tell us anything about y so you can’t say about x-y.
Statement 2 tells that y is a natural number but doesn’t tell you anything about x so you can’t say about x-y.

Now, to check for option 3, we can combine the information from both statements. x is a integer so x=-------, -3, -2, -1, 0, 1, 2, 3------- where as y=1,2,3,4------

Now, depending upon the value that x or y pick in one instance, x-y can be positive or negative so you can’t tell x-y is positive or negative in general.

In this case, the correct option would be 4. So, remember that for a question which is not expecting one definitive answer, even the presence of 2 solutions doesn’t mean that you have got the answer.

[/Solved Example]

Note: In first 3 examples, if there would have been 5 options, nothing to worry. May be the correct options would have been 4, 4 and 5 or something else depending upon the order of option.

The above 3 examples shall be summarised in form of some basic rules while solving DS questions.

Rules to Solve DS Questions

[Points to Remember]

Rule 1. Even ‘no’ can be the answer.

[/Points to Remember]

[Solved Example]

Example 4:
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1: if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2: if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3: if the question can be answered by using either of the statements alone.
Choose 4: if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5: if the question cannot be answered even by using both statements together.

Question: x is a positive integer. Is x=2?
Statement 1: x²-16=0
Statement 2: x is the smallest odd prime number.

Solution:
As per Statement 1, x=4 or -4. Combining with basic data, x is 4. So x is not equal to 2 and you can say with 100% confidence.

Statement 2 tells you that x=3. So x is not equal to 2 and you can say with 100% confidence.

So which option would you choose. Students make mistake to choose 5 as they think that none of the statements gave a x=2. But that was not the question. The examiner asked is x=2 and ‘No’ is also a definite and unique answer.

[/Solved Example]

[Points to Remember]

Rule 2. If a question asks for a numerical value, the question is answerable only if a statement provides data with which one can arrive at a unique value and not a range of values.
[/Points to Remember]

[Solved Example]
Example 5:
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1: if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2: if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3: if the question can be answered by using either of the statements alone.
Choose 4: if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5: if the question cannot be answered even by using both statements together.
Question : x is an integer. What is the value of x
1. x>0
2. x²-25<0

Solution:
As per Statement 1, x is any positive integer so nothing can be found out
From Statement 2, -5< x < 5 again x can be multiple values.
Combining the two statements, x can be 1,2,3 or 4 but not a single value.

So the correct option is (5). Students think that as they have found a set of values for x, it is fine. No, you were supposed to find only one definite value of x.

[/Solved Example]
[Points to Remember]

Rule 3. Though you are not supposed to assume any data not given, the basic formulas of Algebra, Geometry, and Arithmetic can be used to solve questions.

[/Points to Remember]
[Solved Example]
Example6:
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1: if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2: if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3: if the question can be answered by using either of the statements alone.
Choose 4: if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5: if the question cannot be answered even by using both statements together.

Question: In a triangle ABC, Angle (B)=90⁰ . Fine length ( AC)
Statement 1: length ( AB)= 6
Statement 2: length( BC)=8
Combining the two statements and using Pythagoras Theorem, AC=10
Hence, Option 4 is correct.

[/Solved Example]
[PointstoRemember]
Rule 4. The solution to a question can be different from 2 statements but unique in both cases. In this case, both the options are right.

[/Points to Remember]
[Solved Example]
Example:7
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1 if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2 if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3 if the question can be answered by using either of the statements alone.
Choose 4 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5 if the question cannot be answered even by using both statements together.

Question: What is the value of x if x²-5x+6=0?
Statement 1.x>2
Statement 2.x<3
Solution:
x²-5x+6=0 is a quadratic equation whose roots are 2 and 3
Now from Statement 1, x>2 hence x=3 so you get a unique value of x=3 thus Statement 1 alone is sufficient
From Statement 2, x<3 hence x=2 so you get a unique value of x=3 thus Statement 2 alone is sufficient
As you can see, both Statements 1 and 2 are individually sufficient to solve the question though you get different values of x from both cases, so the right option is 3.
[/Solved Example]
[Points to Remember]
Rule 5: Generally, you are not supposed to do very long calculations in DS questions. If you find caught yourself into one, you are on wrong track.

[/Points to Remember]
[Solved Example]

Example:8
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1 if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2 if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3 if the question can be answered by using either of the statements alone.
Choose 4 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5 if the question cannot be answered even by using both statements together.

Question: x is a positive integer. Find the value of x¹³
Statement 1: x is an even number
Statement 2 : x is a prime number.

Now, from Statement 1, x can be 2,4,6,8 and so on...hence x¹³ can take different values
From Statement 2, x can be 2,3,5,7.... and hence x¹³ can take different values
Combining the information of 2 statements with basic data, x=2
So we need to find the value of 2¹³.
Now, many students start finding this value. But do you really need to? As soon as you come to last step, you know that the value of x can be found out with 100% confidence using both statements hence the correct option is 4. Why and where do we need to write the value of 2¹³  ?

[/Solved Example]
Let us see some more examples;
[Solved Example]

Example:9
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1 if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2 if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3 if the question can be answered by using either of the statements alone.
Choose 4 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5 if the question cannot be answered even by using both statements together.

Q. In an election, does Candidate A get the majority of the votes?
I. Candidate B got 49% of the votes.
II.Candidate A got twice as many votes as B and the difference between their votes was 30%
of the total votes.
Solution:
Statement I: Candidate B got 49% of the votes. But there can be a candidate C with 50.9% votes . Hence, Candidate A may or may not have got the majority of the votes. Hence, statement I alone is not sufficient.
Statement II: A = 2B and A – B = 30% of the total.
2B – B = B 30% of the total.
A = 2B = 60% of the total votes.
Hence, statement II alone is sufficient to answer the question.
Ans= (2)
[/Solved Example]

[Solved Example]
Example 10:
Directions: The question below is followed by two statements, I and II. Answer the question using the following instructions:
Choose 1 if the question can be answered by using statement A alone but not by Statement B alone.
Choose 2 if the question can be answered by using statement B alone but not by Statement A alone.
Choose 3 if the question can be answered by using either of the statements alone.
Choose 4 if the question can be answered by using statements together, but cannot be answered using either of the statements alone.
Choose 5 if the question cannot be answered even by using both statements together.
Q. Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up head, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stop?
I. He stops after 21 coin tosses.
II. He obtained three more tails than heads.
Solution: As Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a
blue mark, he would reach Red mark if he takes even steps and blue if he takes odd steps.(This is the concept that you should know from Number Systems, please see yourself why this would happen)
From Statement 1, He takes 21 steps that are odd. So by taking 12 steps to the left and 9 to the right, he would stop at blue mark. (No other combination is possible if he has to stop after 21 steps). So Statement 1 alone is sufficient.
From Statement 2, as he obtained 3 more tails than heads, there are n different combinations possible . But in any case, he can stop at blue only, so you are sure that he would stop at blue only.
Hence, both the statements are individually sufficient.
Ans=(3)
[/Solved Example]
Now let us solve similar questions which appeared in CAT.
Each question is followed by two statements, A and B. Answer each question using the following instructions: (CAT 2008)

Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using either statement alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered on the basis of the two statements

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:
a.    If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.
b.    If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n - 1) players are grouped into (n - 1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.
Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

Q 11. What is the number of matches played by the champion?
A.    The entry list for the tournament consists of 83 players.
B.    The champion received one bye.
a) 1
b) 2
c) 3
d) 4
e) 5
Solution: (d)
If we consider statement A alone, the entry list consists of 83 players. In round 1, one of the 83 players gets a bye and directly moves to the next round. Thus, 42 players move to round 2. Similarly, 21 players move to round 3, 11 to round 4, 6 to round 5, 3 to round 6 and 2 to round 7. The winner of the tournament would have played one match in each of the rounds i.e. 7 matches, provided he does not get a bye. Since we do not know whether the champion got a bye or not, we cannot answer on the basis of statement A alone.
From statement B, the champion received one bye. We cannot determine the number of matches played by him. So, statement B alone is not sufficient.
From A and B together, the player got one bye, so he must have played only 6 matches. So, we can answer the question by using both statements A and B.

Q12. If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?
A.    Exactly one player received a bye in the entire tournament.
B.    One player received a bye while moving on to the fourth round from the third round
a) 1
b) 2
c) 3
d) 4
e) 5
Solution: (d)
From statement A alone, exactly one player received a bye in the tournament. We get many values of n between 65 and 128 that satisfy this condition. E.g. n can have value 124 in round 1 to follow the pattern – 124, 62, 31, 16, 8, 4, 2, 1
N can also have the value 127 following the pattern – 127, 64, 32, 16, 8 , 4, 2, 1
Thus, statement A alone is not sufficient.
From B, one player received a bye while moving from round 3 to 4. Here also we can have multiple values of n. E.g. n can have value 124 in round 1 where 1 player received a bye while moving from round 3 to 4 – 124, 62, 31, 16, 8, 4, 2, 1
Also, n can have value 122 in round 1 – 122, 61, 31, 16, 8, 4, 2, 1
Thus, statement B alone is not sufficient.
Taking A and B together, n can only have the value 124 in round 1, where exactly one player received a bye while moving from round 3 to 4 following the pattern – 124, 62, 31, 16, 8, 4, 2, 1
Thus, we can answer the question using both A and B together.

The following question appeared in (CAT 2000)
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together

Q 13. Consider three real numbers, X, Y and Z. Is Z the smallest of these numbers?
A.    X is greater than at least one of Y and Z.
B.    Y is greater than at least one of X and Z.
a) 1
b) 2
c) 3
d) 4
Solution: (c)
From A, there are 4 possibilities:
X>Y>Z
X>Z>Y
Z>X>Y
Y>X>Z
Thus, A alone is not sufficient.
From B, there are 4 possibilities:
Y>X>Z
Y>Z>X
X>Y>Z
Z>Y>X
Thus, B alone is not sufficient.
Taking A and B together, we get
Either X>Y>Z or Y>X>Z
In both cases, Z is smallest, hence option (c)

Q 14. Let X be a real number. Is the modulus of X necessarily less than 3?
A.    X(X + 3) < 0
B.    X(X – 3) > 0
a) 1
b) 2
c) 3
d) 4
Solution: (a)
X(X+3) < 0
=> -3 <X < 0
=> |X| < 3
=> A alone is sufficient
X(X-3) > 0
=> X < 0 or X > 3
=> No unique answer
Hence, option (a)

Q 15. How many people are watching TV programme P?
A.    Number of people watching TV programme Q is 1000 and number of people watching both the programmes, P and Q, is 100.
B.    Number of people watching either P or Q or both is 1500.
a) 1
b) 2
c) 3
d) 4
Solution: (c)
From A, Q = 1000
P  Q = 100
This does not give any information regarding how many people are watching TV.
From B, P U Q = 1500
This statement alone is not sufficient.
Combining A and B, we have
P U Q = P + Q - P  Q
1500 = P + 1000 – 100
P = 600, hence option (c)

Q 16. Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?
A.    Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
B.    Diameter of the circumscribed circle of the triangle PQR is equal to 18 cm
a) 1
b) 2
c) 3
d) 4
Solution: (c)
From A, PF = PR – FR = PR – OD = PR – 5
QD = QR – DR = QR – OF = QR – 5
=> PE = PF and QE = QD
=> PE = PR – 5 and QE = QR – 5
=> PQ = PE + QE = PR – 5 + QR – 5
=> PR + QR = PQ + 10
=> This statement alone is not sufficient.
From B, diameter of circumscribing circle = hypotenuse
=> PQ – 18
=> PR² + RQ² = PQ²
But this does not give PR + RQ

Combining both statements,
PR + QR = PQ + 10 = 18+10 = 28
Hence, option (c)

Q 17. Harshad bought shares of a company on a certain day, and sold them the next day. While buying and selling he had to pay to the broker one percent of the transaction value of the shares as brokerage. What was the profit earned by him per rupee spent on buying the shares?
A.    The sales price per share was 1.05 times that of its purchase price.
B.    The number of shares purchased was 100.
a) 1
b) 2
c) 3
d) 4
Solution: (a)
From A, cost of buying shares for Harshad is CP + 0.01CP = 1.01CP
Cost of selling shares for Harshad is SP – 0.01 SP = 0.99SP
Profit = cost of selling – cost of buying = 0.99SP – 1.01 CP
= 0.99x1.05CP – 1.01CP
= 0.0295CP
Thus, profit earned per rupee spent on buying shares is 0.0295
From B, we cannot conclude anything, hence option (a).

Q 18. For any two real numbers
a  b = 1 if both a and b are positive or both a and b are negative.
   = –1 if one of the two numbers a and b is positive and the other negative.
What is (2  0)  (–5  –6)?
A.    a  b is zero if a is zero.
B.    a  b = b  a
a) 1
b) 2
c) 3
d) 4
Solution: (c)

= 0, hence both statements are required.

Q 19. There are two straight lines in the x-y plane with equations ax + by = c , dx + ey = f. Do the two straight lines intersect?
A.    a, b, c, d, e and f are distinct real numbers.
B.    c and f are non-zero
a) 1
b) 2
c) 3
d) 4
Solution: (d)
Statement A implies that a, b, c, d, e, f are real distinct numbers.
But if a/d = b/e = c/f then lines might be parallel or might not intersect at all.
Thus, A alone is not sufficient.
B implies that equations are not homogenous.
Thus, B is also not sufficient.
Condition for intersecting lines is a/d b/e
Even after combining, the condition is not clear, hence option (d).

Q 20. O is the centre of two concentric circles. ae is a chord of the outer circle and it intersects the inner circle at point; b and d. c is a point on the chord in between b and d. What is the value ofac/ce?
A.    bc/cd = 1
B.    A third circle intersects the inner circle at b and d and the point c is on the line joining the centres of the third circle and the inner circle
a) 1
b) 2
c) 3
d) 4
Solution: (b)
From A, bc = cd
If c is the mid point of bd, it would also be the mid point of ae as the circles are concentric.
Thus, ac = ae
Thus, A alone is sufficient.
From B, if c is the mid point on the line joining the two centres, it has to bisect chord bd.
Thus, c will also bisect the chord ae as circles are concentric.
=> ac = ce
=> B alone is sufficient, hence option (b).

Q 21. Ghosh Babu has decided to take a non-stop flight from Mumbai to No-man’s-land in South America. He is scheduled to leave Mumbai at 5 am, Indian Standard Time on December 10, 2000. What is the local time at No-man’s-land when he reaches there?
A.    The average speed of the plane is 700 kilometres per hour.
B.    The flight distance is 10,500 kilometres
a) 1
b) 2
c) 3
d) 4
Solution: (d)
By using both statements together, we can get the duration of the flight, but for the arrival time we require time zone difference between Mumbai and no man’s land.
Hence, option (d).

Q 22. What are the ages of two individuals, X and Y?
A.    The age difference between them is 6 years.
B.    The product of their ages is divisible by 6.
a) 1
b) 2
c) 3
d) 4
Solution: (d)
From A, X – Y = 6
From B, XY is divisible by 6
Thus many values are possible like (12, 6), (18, 12), (24, 18)
Thus the question cannot be answered even by using the statements together. Hence option (d).