MathRevolution wrote:

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Math Revolution GMAT math practice question]

Is \(0\) between \(x\) and \(y\)?

\(1) x-y>0\)

\(2) x^2-y^2>0\)

Target question: Is 0 between x and y? Statement 1: x - y > 0 This statement doesn't FEEL sufficient, so I'll TEST some values.

There are several values of x and y that satisfy statement 1. Here are two:

Case a: x = 2 and y = -1. In this case, the answer to the target question is

YES, 0 IS between x and yCase b: x = 2 and y = 1. In this case, the answer to the target question is

NO, 0 is NOT between x and ySince we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: x^2 - y^2 > 0 This statement doesn't FEEL sufficient, so I'll TEST some values.

IMPORTANT: When testing values always check to see whether you can RE-USE values you used when analyzing the other statement.

We can see that we can RE-USE both of the cases that we used for statement 1. That is the x- and y-values we used for statement 1 also satisfy statement 2.

Case a: x = 2 and y = -1. In this case, the answer to the target question is

YES, 0 IS between x and yCase b: x = 2 and y = 1. In this case, the answer to the target question is

NO, 0 is NOT between x and ySince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the

same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.

In other words,

Case a: x = 2 and y = -1. In this case, the answer to the target question is

YES, 0 IS between x and yCase b: x = 2 and y = 1. In this case, the answer to the target question is

NO, 0 is NOT between x and ySince we cannot answer the

target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com