Solutions

Get detailed explanations to advanced GMAT questions.

Question

If a, b, x and y are positive integers, is a^(-x) > b^(-y) ?

I. a < b

II. x < y

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Easy

Solution

Option C is the correct answer.

Option Analysis

We need to find a definite YES or NO.

Statement I is insufficient: a < b If a=2 and b = 8 and x = 1 and y = 1 then YES. But if a = 2 and b = 8 and x = 100 and y = 1 then NO. Insufficient.

Statement II is insufficient: x < y If a = 2 and b = 8 and x = 1 and y = 2 then YES. But if a = 100 and b = 1 then NO. Insufficient.

Together I and II, a < b and x < y,

We know that b>a and y>x. Thus:

1.b^y>a^y

2.a^y>a^x

Thus, b^y>a^x. Sufficient.