PWN Test Prep SAT Q&A

pwnthetest — Fri, 12 Jul 2024 08:12:42 -0400

Try (12+x)(16+x)=285, where x is the width of the walkway. :)

If x3 = y, andy > x > 0, then what is the difference between x6 and x3, in terms of y ?

pwnthetest — Sun, 01 Oct 2023 10:42:32 -0400

If x^3 = y, then square both sides to get x^6 = y^2.

From there, we find the difference between x^6 and x^3 by subtracting: x^6 - x^3. Then we just substitute:

x^6 - x^3 = y^2 - y

in the xy plane, the line determined by the points (8,3) and (a,b) passes through the origin. If a isn’t equal to zero, what is b/a ?

pwnthetest — Fri, 06 Aug 2021 10:52:16 -0400

When a line passes through the origin, all of the points on the line (other than the origin) tell you the slope. So the answer here is 3/8.

Think of it this way. You can calculate the slope using the two points you know: (0, 0) and (8, 3). Use the slope formula:

(3 – 0)/(8 – 0) = 3/8

That same slope must apply for any other point on the line, like (a, b):

(b – 0)/(a – 0) = 3/8
b/a = 3/8

8 persons paint 8 rooms in 8 days .how many days it will takes 1 man to paint 1 room?

pwnthetest — Fri, 02 Jul 2021 13:01:34 -0400

8 days.

The number of boys in a class has increased by 20% compared to the previous year and that of girls has decreased by 20% . There is now one more than before in this class. number of students this year?

pwnthetest — Fri, 02 Jul 2021 12:31:54 -0400

You can’t solve this to precisely one number, but you can identify a number of integer solution sets. If this were a real test question it would be worded to say something like “which of the following could be the number of students this year?”

Let’s say the class had b boys and g girls last year.

This year, there’s one more kid in the class, so the total should be b + g + 1.

We also know, however, that the numbers of boys and girls changed: this year there are (1 + 0.2)b boys and (1 – 0.2)g girls.

We can set those two expressions equal and simplify.

b + g + 1 = (1 + 0.2)b + (1 – 0.2)g
b + g + 1 = 1.2b + 0.8g
1 = 0.2b – 0.2g
5 = b – g

That’s as far as you can get, so now you’re just left with possible sets that can work. For example, there could have been 15 boys and 10 girls last year, which would mean there are b + g + 1 = 26 students this year.

Any numbers you pick for b and g that are multiples of 5 will give you integer values for the number of boys and girls this year, because multiples of 5 can be increased/decreased by 20% and stay integers.

From the set of integers from 1 to 10 inclusive two integers are randomly selected one after the other with replacement what is the probability that the sum of the two integers are greater than 5

pwnthetest — Mon, 05 Apr 2021 23:11:15 -0400

It’s easier to figure out the probability of the sum being 5 or less, and then you can subtract that from 1 to find the answer you actually want.

To get 5 or less, you can only have these two pulls:

1, 1
1, 2
1, 3
1, 4
2, 1
2, 2
2, 3
3, 1
3, 2
4, 1

That’s 10 possible outcomes of 5 or less. Out of how many total outcomes?

Well, you have 10 possible numbers to select, and you’re selecting with replacement, so there are 10*10 = 100 outcomes.

if 10 of them are 5 or less, then there’s a 10% chance of pulling 5 or less. Which means there’s a 90% chance of pulling more than 5.

if x is a positive integer n if there are exactly x+2 integers greater than x and less than x^2 then x

pwnthetest — Mon, 05 Apr 2021 23:05:33 -0400

Just do trial and error here.

2^2 = 4, there’s only one integer between 2 and 4.

3^2 = 9, there are five integers between 3 and 5 (4, 5, 6, 7, and 8). So x = 3.

The inequality -6≤x≤3 is a segment graphed on the x axis, and the inequality -4≤y≤8 is a segment graphed on the y axis. What is the area of the quadrilateral formed in the xy plane by joining the endpoint of the graphs?

pwnthetest — Wed, 02 Dec 2020 22:17:40 -0500

I knew this one sounded familiar! See here from a couple years ago: https://qa.pwntestprep.com/post/152242806550/the-inequality-6-x-3-is-a-segment-graphed-on

In the triangle ABD shown above, AC bisects angle DAB. Which of the following is equivalent to the ratio AD:DC . A) x:z B) y:z C) z:x D) z:y

pwnthetest — Wed, 23 Sep 2020 10:40:10 -0400

figure?

What is the number of cubic inches in 1 foot

pwnthetest — Fri, 18 Sep 2020 11:56:52 -0400

I think you mean in a CUBIC foot--you can’t compare cubic inches to feet diresctly.

There are 12 inches in a foot, so there are 12 × 12 × 12 = 1728 cubic inches in a cubic foot.

In the figure above PQRSTU is a regular hexagon. If the area of triangle QSU is root 3, what is the are of the hexagon.

pwnthetest — Thu, 10 Sep 2020 21:49:39 -0400

Can you upload an image of the figure? Use the Disqus comments under this post.

The Math Guide is (basically) back in stock at Amazon

pwnthetest — Tue, 26 May 2020 11:24:11 -0400

The Math Guide is (basically) back in stock at Amazon

Extending 3-month Math Guide Online subscriptions

pwnthetest — Sun, 19 Apr 2020 10:22:00 -0400

Extending 3-month Math Guide Online subscriptions

Three bags of potato chips cost m cents. At this rate, what is the cost, in cents, of one bag of chips.

pwnthetest — Thu, 02 Apr 2020 08:02:04 -0400

If three bags cost m cents, then each bag costs one third of that: m/3.

If this isn’t clicking for you, try plugging in a real number for m. Say three bags of chips cost 60 cents. Then each bag must cost 60/3 = 20 cents.

Meredith leans a 15 foot ladder against a wall. The base of the ladder is 4.75 feet from the base of the wall. Of the following, which length,in feet, is closest to the height of the top of the ladder along the wall? A)3.16 B)3.87 C)14.23 D)15.73

pwnthetest — Sat, 29 Feb 2020 08:53:01 -0500

This is a right triangle question. The hypotenuse is 15 and the leg on the ground is 4.75. What’s the other leg?

4.75^2 + x^2 = 15^2
22.5625 + x^2 = 225
x^2 = 202.4375
x = 14.22805...

In the xy-plane, the graph of the cubic equation y=x^3+ax^2+bx+c, where a,b, and c are constants, has x-intercept at x=-4, x=-5, and x=-7. What is the value of a?

pwnthetest — Sat, 29 Feb 2020 08:50:03 -0500

The x-intercepts tell you the factors, and because the leading term (x^3) has a coefficient of 1 you know there are no constants being multiplied through the whole thing. So you know the factored version of the equation is:

y = (x + 4)(x + 5)(x + 7)

Multiply that out.

y = (x^2 + 9x + 20)(x + 7)
y = x^3 + 9x^2 + 20x + 7x^2 + 63x + 140
y = x^3 + 16x^2 + 83x + 140

So a = 16.

How is (-4x^3)^2/3 equivalent to 2x^2(2^1/3)?

pwnthetest — Sat, 29 Feb 2020 08:45:23 -0500

Then just rearrange.

The sun converts mass into energy at a rate of 4.29x10^9 kg per second. In one day, how much mass, in kg, is converted into energy by the sun?

pwnthetest — Sat, 29 Feb 2020 08:37:34 -0500

Just figure out how many seconds there are in a day, then multiply it by that big number.

There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.

60 × 60 × 24 = 86,400 seconds in a day.

The function f is defined by the equation f(x)=x(x-b)^2, where b is a constant. If f(5)=f(9), what is the value of f(1)?

pwnthetest — Sun, 23 Feb 2020 08:33:58 -0500

Use the given fact that f(5) = f(9):

5(5 - b)^2 = 9(9 - b)^2
5(25 - 10b + b^2) = 9(81 - 18b + b^2)
125 - 50b + 5b^2 = 729 - 162b + 9b^2
0 = 604 - 112b + 4b^2
0 = 151 - 28b + b^2
0 = b^2 - 28b + 151

Do the quadratic formula on that and you’ll see that b = 14 ± 3√5, so there will actually be two possible values of f(1), neither of which is the kind of neat and tidy answer you’d expect from an SAT question.

The value of x is more than the value of y. The sum of 3x and 4y is 20 less than the value of 8x. What is the value of x?

pwnthetest — Sun, 23 Feb 2020 08:23:08 -0500

3x + 4y = 8x – 20
4y = 5x – 20
y = 5/4x – 5

That’s all you can do here. You don’t have two equations (knowing that x > y alone doesn’t count) so you can’t solve this as you’ve submitted it. Any point on the line below gives you a possible solution.