Data Sufficiency

ziyuenlau wrote:Is x² > y²?

(1) x > y
(2) x > 0

Target question: Is x² > y²?

Statement 1: x > y
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 which case x² = 2² = 4, and y² = 1² = 1. So, x² > y²
Case b: x = 2 and y = -3, in which case x² = 2² = 4, and y² = (-3)² = 9. So, x² < y²
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x > 0
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1, in which case x² = 2² = 4, and y² = 1² = 1. So, x² > y²
Case b: x = 2 and y = -3, in which case x² = 2² = 4, and y² = (-3)² = 9. So, x² < y²
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTICE that we used the same counter-examples to show that statements 1 and 2 alone are not sufficient.
So, we can use the same cases to show that the statements COMBINED are also not sufficient.
Case a: x = 2 and y = 1, in which case x² = 2² = 4, and y² = 1² = 1. So, x² > y²
Case b: x = 2 and y = -3, in which case x² = 2² = 4, and y² = (-3)² = 9. So, x² < y²
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Hi ziyuenlau,

This question can be solved by TESTing VALUES. When squared terms show up in DS questions, it's important to remember to consider NEGATIVE values along with the positive/zero values that will automatically come to mind.

We're asked if X^2 is greater than Y^2. This is a YES/NO question.

1) X > Y

IF...
X=1, Y=0
then the answer to the question is YES.

IF...
X=1, Y= -2
then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) X > 0

Notice how both TESTs from Fact 1 also "fit" Fact 2... so no additional work is required here.

IF...
X=1, Y=0
then the answer to the question is YES.

IF...
X=1, Y= -2
then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that fit both Facts and provide two different answers to the given question (one YES and one NO).
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich