# "Cracking the GRE" Error?

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Hello all,

I am studying for the GRE, which I am taking at the end of the month.

Right now I'm working through the Princeton Review 'Cracking the GRE' book and I've run into what I think is an egregious error in the answer key for the 'Real World Math Drill', but maybe I am missing something obvious;

Question;

"5x – 2y = 2y – 3x
Quantity A       Quantity B
x                        y
A.Quantity A is greater.
B.Quantity B is greater.”
C.The two quantities are equal.
D.The relationship cannot be determined from the information given.”

“  5. D
Variables in the question stem means to plug in. For this problem, it’s easier to plug in if you simplify the equation first. Rearrange the equation to put the variables on opposite sides of the equal sign. 8x = 4y. Then divide both sides by 4 to get that 2x = y. Now, choose some easy numbers such as x = 2 and y = 4. In this case, Quantity B is greater, so eliminate answers (A) and ©. Next, try something like x = 0 and y = 0. In this case, the two quantities are equal. Eliminate choice ( and the correct answer is (D).”

Excerpt From: Princeton Review. “Cracking the GRE Premium Edition with 6 Practice Tests, 2015 (Graduate School Test Preparation).”

This does not seem right at all... after rereading the answer key I am 99.9% sure that it is wrong (for example, if you plug in x=2 and y=4 as the answer suggests, the terms in 2x=y are equal. Also, I'm not sure why they think they can just plug zeros in for x and y). Also I have no idea what the first sentence in their paragraph is supposed to mean.

Can someone either confirm that this is a mistake or try to point out what I'm missing.

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When doing comparison questions, the best way to do so is if you replace the variables into any integer, and by that it can mean 0, odd, even, and their negative equivalents (e.g., 2, -2, 3, -3). That's what Princeton is referring to by "plug in", change the x and y in the question to actual numbers

After you simplify, the equation is 2x = y

Let's try zeroes first:

if x = 0, y = 0

2(0) = 0

0 = 0

Therefore, x = y

Let's try x > y now

if x = 4, y = 3

2(4) = (3)

8 = 3

Now mathematically these things don't really make a lot of sense, but that's why the answer is D. Without telling you more, it's sort of like saying 2 apples equals 1 orange. You can't tell if that's true or not if you didn't know what the price of the apples and oranges were to begin with right? Similar idea here. Plugging/replacing the variables with any two integers can give you a myriad of answers that can range from x and y equalling (e.g. both = 0), x > y, or even y > x

Another way of looking at it is the fact that answers A, B, and C can all be right in any different situation. When you do more questions you realize that if any two of these three answers are right, then it has to be D. Something can't be bigger (as indicated in answer A), if they can also be smaller (as indicated in answer , right?

Hope that helps!

Edited by Jay's Brain
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Without telling you more, it's sort of like saying 2 apples equals 1 orange. You can't tell if that's true or not if you didn't know what the price of the apples and oranges were to begin with right? Similar idea here. Plugging/replacing the variables with any two integers can give you a myriad of answers that can range from x and y equalling (e.g. both = 0), x > y, or even y > x

Another way of looking at it is the fact that answers A, B, and C can all be right in any different situation. When you do more questions you realize that if any two of these three answers are right, then it has to be D. Something can't be bigger (as indicated in answer A), if they can also be smaller (as indicated in answer , right?

Aha, yes that makes sense. I hadn't seen this type of problem before but I understand what they expect now. Thanks for the response.

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