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
