Is x^2 > y^2? (1) x > y (2) x > 0

[hazelnut01]

Is x^2 > y^2?

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

Source : Manhattan
OA=E

[Brent@GMATPrepNow]

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

[[email protected]]

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