tag:blogger.com,1999:blog-47464261888121096462014-10-02T01:42:10.730-04:00Got a GMAT or GRE math question? Email me and I'll explain it!ggnoreply@blogger.comBlogger367125tag:blogger.com,1999:blog-4746426188812109646.post-33570398806495814032011-05-23T14:10:00.001-04:002011-05-23T14:10:00.234-04:00

A rectangular shed has a perimeter of 40 meters and a diagonal length of 15 meters. What is the area of the shed in square meters?(A) 120(B) 106.5(C) 93.5(D) 87.5(E) 80Let's say the width of the shed is W and the length is L. Then we know that2W + 2L = 40, or W + L = 20 andW2 + L2 = 152 = 225.If we square both sides of the first equation, we get(W+L)2 = 400W2 + L2 + 2WL = 400.Since we know that

ggnoreply@blogger.com1tag:blogger.com,1999:blog-4746426188812109646.post-90524438595778601182011-05-18T14:00:00.000-04:002011-05-18T14:00:03.337-04:00

Let A, B, C, and D be digits 0-9. If AB and CD represent two 2-digit numbers, is (AB)(CD) odd?(1) A + C = 9(2) B + D = 9The product of two numbers is odd only when both numbers are odd. And since even/odd depends only on the last digit of a number, this means that (AB)(CD) will be odd only when (B)(D) is odd. Statement 1 is insufficient because it gives us no information about B or D.Statement

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-49612496131911574872011-05-14T14:39:00.000-04:002011-05-14T14:39:00.122-04:00

a and b are positive integers and [(a1/4)(b1/3)]12 = 2000. What is a+b?(A) 200(B) 108(C) 50(D) 12(E) 7The expression [(a1/4)(b1/3)]12 can be rewritten as [(a3)(b4)]. To determine the values of a and b, we should start by factoring 2000 into its prime factors. Notice that 2000 = (10)(10)(10)(2) = 2 x 5 x 2 x 5 x 2 x 5 x 2, or 2453. So the only possible solution is a=5 and b=2. Therefore a+b =

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-80968151630662425252011-05-10T15:48:00.000-04:002011-05-10T15:48:01.422-04:00

Suppose a, b, and c are positive numbers, and a/b = 4, b/c = 3. What is (a+2b+3c)/(a+b+c)?(A) 21/16(B) 19/16(C) 17/12(D) 17/8(E) 11/8We can replace a and b with expressions in terms of c. Since b/c = 3, we have b = 3c. And since a/b = 4, we have a/(3c) = 4, or a = 12c. Then the fraction becomes(12c + 6c + 3c)/(12c + 3c + c) = (21c)/(16c) = 21/16.So the correct answer is A.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-57221315421344313262011-05-06T13:57:00.000-04:002011-05-06T13:57:00.190-04:00

What is the largest integer x such that 37x54x divides evenly into 4547?(A) 12(B) 11(C) 10(D) 8(E) 7Note that 4547 = (325)47 = 394547.37x54x will divide evenly into 394547 so long as 7x ≤ 94 and 4x ≤ 47.Since 94/7 = 13.### and 47/4 = 11.###, the largest allowable value for x is 11.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-72873735279824987252011-05-02T13:18:00.000-04:002011-05-02T13:18:00.192-04:00

A cube's surface area in square centimeters is 3 times its volume in cubic centimeters. What is the side length of the cube?(A) 1 cm(B) 1.5 cm(C) 2 cm(D) 2.4 cm(E) 3 cmLet's call the side length of the cube x. There are 6 faces of a cube, and each face has an area of x2 square centimeters. Thus, the surface area of the cube is 6x2.The volume of the cube is x3.Since the surface area is 3 times

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-21325592745514468322011-04-29T12:22:00.000-04:002011-04-29T12:22:00.354-04:00

Ellen invites 5 people to dinner, 2 women and 3 men. If Ellen's dining table is circular and the guests choose their seats at random around her table, what is the probability that no female is seated next to another female?(A) 1/90(B) 1/72(C) 5/72(D) 5/36(E) 1/10If there are 3 females and 3 males total, and no female is seated next to another female, then the people are arranged in alternating

ggnoreply@blogger.com2tag:blogger.com,1999:blog-4746426188812109646.post-83392124102118031562011-04-25T12:53:00.000-04:002011-04-25T12:53:01.012-04:00

(Col A) (4 + |x|4)/(-2 - |x|7)(Col B) (-2 - |x|4)/(-4 - |x|2)Regardless of what the values of x is the quantity |x| is always positive. The quantities -2 - |x|7, -2 - |x|4, and -4 - |x|2 are always negative; the expression 4 + |x|4 is always positive. Thus, Column A is a negative number and Column B is a positive number. So the answer is B.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-3202506703286878962011-04-21T13:25:00.001-04:002011-04-22T20:26:26.981-04:00

If x and y are unequal, what is the value of xy?(1) x3 + y = 11x(2) y3 + x = 11yAs the two statements are symmetric, it is not possible that (1) is sufficient on its own but (2) is insufficient, and vice versa. Nor are are they both sufficient independently, so the answer must be either C or E.If we combine the information from the two statements, we havex3 + y = 11x, andy3 + x = 11yAdding the

ggnoreply@blogger.com1tag:blogger.com,1999:blog-4746426188812109646.post-58883210016345892132011-04-17T14:18:00.001-04:002011-04-17T14:18:00.207-04:00

How many integers between 10 and 1000 are divisible by 6 and palindromes? (Palindromic numbers are the same written forwards and backwards.)(A) 24(D) 22(C) 18(D) 14(E) 12A number that is divisible by 6 must be divisible by both 2 and 3. Numbers that are divisible by 2 end in 0, 2, 4, 6, or 8. For numbers that are divisible by 3, all the digits must add up to a multiple of 3. Since we are

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-746259121807647742011-04-13T13:14:00.000-04:002011-04-13T13:14:00.332-04:00

If x and y are negative integers and z is a positive integer greater than 1, which of the following expressions are never integers?(i) sqrt(xy + z)(ii) z^(x+y)(iii) (z + 0.5)/(x + y + 0.5)(A) i(B) i and ii(C) ii(D) ii and iii(E) iiiStatment (i) is easy to eliminate. There are many possible values of x, y, and z that will make xy+z a square number, and hence sqrt(xy+z) an integer. For example,

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-49605616849071841542011-04-08T13:21:00.000-04:002011-04-08T13:21:00.187-04:00

An isosceles triangle T has a perimeter of 14 and integer side lengths. For all the possible triangular shapes of T, what is the range of their areas?(A) 3.5(B) sqrt(7)(C) 2sqrt(21) - sqrt(35)(D) 3sqrt(7) - sqrt(35)(E) 3sqrt(7) - sqrt(14)There are only 3 possible dimensions for T:6, 4, 44, 5, 52, 6, 6The triangle with sides 6, 4, and 4 has an area of 3sqrt(7).The triangle with sides 4, 5, and 5

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-37870982157104104722011-04-04T13:02:00.000-04:002011-04-04T13:02:00.161-04:00

Rectangle R has a perimeter of 14 and integer side lengths. What is the average area of all the possible rectangular shapes of R?(A) 14(B) 8(C) 33/4(D) 28/3(E) 15/2There are only 3 possible shapes of R. It can be either a 1x6, 2x5, or 3x4 rectangle. These rectangles have areas of 6, 10, and 12 respectively. Since (6+10+12)/3 = 28/3, the correct answer is D.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-60734926705154164482011-03-31T12:01:00.002-04:002011-03-31T12:01:00.202-04:00

If x ≠ y and x2 - 4x = 2xy - y2 - 4y, which of the following must be true?(A) x - y = 4(B) x2 + y2 = 16(C) x = 2y(D) 4x + 4y = xy(E) 4x = y2For this problem, we need to find the answer choices that is true based on the fact that x ≠ y and x2 - 4x = 2xy - y2 - 4y. If we rearrange the equation and put the more complex terms on one side, we getx2 - 2xy + y2 = 4x - 4y.This can be factored into(x-y

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-26678887295370052172011-03-27T13:02:00.000-04:002011-03-27T13:02:00.879-04:00

p, q, and r are distinct prime numbers. Is pqr an even number?(1) p+q = r(2) r = 13The question is really asking if one of the numbers p, q, or r equals 2, since 2 is the only number that is both even and prime. If one of them is equal to 2, the product pqr will be even. If they are all odd primes, pqr will not be even.Statement 1: If p+q = r, then either p or q must be equal to 2. If p and

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-32738306866489824362011-03-23T12:43:00.000-04:002011-03-23T12:43:00.759-04:00

(15^x)(6^y)(10^z) = (5^8)(3^9)(2^11). What is x+y+z? ... Note that(15^x)(6^y)(10^z) = (5^x)(3^x)(3^y)(2^y)(5^z)(2^z)= [5^(x+z)][3^(x+y)][2^(y+z)]So we havex+z = 8x+y = 9y+z = 11If we add all the equations together, we get2x + 2y + 2z = 28,and if we divide by 2, we getx+y+z = 14.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-43883728744249254002011-03-19T12:40:00.000-04:002011-03-19T12:40:00.243-04:00

It takes Hal X minutes to swim Y meters, and it takes Sally X minutes to swim 1.5Y meters. Hal and Sally swim a relay race of 5Y meters where Sally swims for twice as much time as Hal. How much of the distance does Sally swim?(A) 25%(B) 30%(C) 45%(D) 64%(E) 75%Hal's rate is Y/X meters per minute, and Sally's rate is 1.5Y/X meters per minute. Let H be the number of minutes that Hal swims and

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-16070344376807829752011-03-14T13:27:00.002-04:002011-03-14T13:27:00.733-04:00

x and y are integers and (x-4)(y-3) = 1.(Col A) 2.5xy(Col B) x2 + y2If x and y are integers, then so are x-4 and y-3. Thus, there are only a finite number of solution sets to this equation. In fact, there are just two!x = 5 and y = 4, since (5-4)(4-3) = (1)(1) = 1x = 3 and y = 2, since (3-4)(2-3) = (-1)(-1) = 1In the first set, 2.5xy = (2.5)(5)(4) = 50, and x2 + y2 = 52 + 42 = 41. So Column A

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-36961930789663913742011-03-10T13:29:00.002-05:002011-03-10T13:29:01.242-05:00

Jill has 25% more money in savings than Dan. If Jill gave Dan $7000, Jan would have 20% less than Dan. How much more money does Jill have than Dan?(A) $8400(B) $7000(C) $1750(D) $1400(E) $1000Let Jill's current savings be J and Dan's savings be D. The question gives us two equations in the variables J and D:J = 1.25D, and(J - 7000) = 0.8(D + 7000), or equivalently J = 0.8D + 12600Notice if we

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-47672412139044567612011-03-06T13:00:00.000-05:002011-03-06T13:00:04.800-05:00

If |x| + |y| ≤ x|y-3|, which of the following must be true?(i) x is not negative(ii) |4x+y| ≤ |xy|(iii) |-x| + |y| ≤ |3x-xy|(A) i(B) i and iii(C) ii(D) ii and iii(E) i, ii, and iiiStatement (i) is the easiest to check. The left side of the equation, |x| + |y|, is always a non-negative number. Therefore, if x|y-3| is at least as large as |x| + |y|, it must be true that x is not a negative number

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-9387756108252750402011-03-02T13:00:00.000-05:002011-03-02T13:00:02.977-05:00

A company has 160 employees. 40% of the employees are part-time, and 30% of the employees are female. How many more full-time male employees are there than part-time female employees?(A) 48(B) 40(C) 32(D) 30(E) not enough informationWe have 4 categories of employees: female part-time, female full-time, male part-time, and male full-time. Since (0.4)(160) = 64, we have 64 part-timers, and since

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-15083769633010554182011-02-27T13:00:00.000-05:002011-02-27T13:00:04.759-05:00

If (4x+y)(x+4y) = 25xy + 400, what is the value of |x-y|?(A) 10(B) 12(C) 20(D) 24(E) 25Since (4x+y)(x+4y) = 4x2 + xy + 16xy + 4y2, we have4x2 + 17xy + 4y2 = 25xy + 4004x2 - 8xy + 4y2 = 400(2x-2y)2 = 4002|x-y| = 20 (taking positive square root of both sides)|x-y| = 10So the correct answer is A

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-48494220417611560032011-02-23T13:39:00.000-05:002011-02-23T13:39:00.161-05:00

R, U, and T are numbers greater than 2. Is R/(UT) greater than 4?(1) R/U + R/T is not greater than 8(2) R/(U-T) is not less than 9Statement 1 can be rearranged as follows:R/U + R/T ≤ 8UT(R/U + R/T) ≤ UT(8)RT + RU ≤ 8UTR(U+T) ≤ 8UTR/(UT) ≤ 8/(U+T)Since U and T are both larger than 2, the quantity 8/(U+T) is less than 8/(2+2) = 2. So Statement 1 tells us that R/(UT) is not greater than 4.

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-75286756932641244982011-02-18T13:30:00.000-05:002011-02-18T13:30:01.795-05:00

The figure above shows three mutually tangent circles. The largest circle has a radius of 3, the medium sized circle has a radius of 2, and the smallest circle has a radius of 1. If the centers of the circles are connected to form a triangle, what is the area of the triangle?(A) 2sqrt(6)(B) 3sqrt(6)(C) 2sqrt(3)(D) 6sqrt(2)(E) 6If we draw straight lines connecting the centers, we end up with a

ggnoreply@blogger.com0tag:blogger.com,1999:blog-4746426188812109646.post-18357192764627741432011-02-14T13:17:00.001-05:002011-02-14T13:17:00.611-05:00

The operation # is defined by the equation a#b = ab/(1 + |a-b|). If x#5 ≤ x, which of the following is true of x?(A) 1 ≤ x ≤ 9(B) 0 ≤ x ≤ 1(C) x ≤ 1(D) 0 ≤ x ≤ 1 or x ≥ 9(E) x ≥ 9If x#5 ≤ x, then 5x/(1 + |x-5|) ≤ x. Since the quantity in the denominator is always a positive number, we can multiply both sides of the inequality by (1 + |x-5|) without changing the direction of the inequality. So

ggnoreply@blogger.com0