Max@Math Revolution wrote:
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 y
Case b: x = 2 and y = 1. In this case, the answer to the target question is
NO, 0 is NOT between x and y
Since 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: https://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 y
Case b: x = 2 and y = 1. In this case, the answer to the target question is
NO, 0 is NOT between x and y
Since 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 y
Case b: x = 2 and y = 1. In this case, the answer to the target question is
NO, 0 is NOT between x and y
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
