# Solutions

Get detailed explanations to advanced GMAT questions.

### Question

If r is an integer, what is the value of 3^(2r)/ 27^(r-1)?

I. 2^r = 32

II. r^2 – 4r = 5

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:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

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

Medium

### Solution

Option A is the correct answer.

### Option Analysis

Given: 3^(2r)/ 27^(r-1),

3^2r/3^3(r-1) = 3^2r–3r+3 = 3^3-r

So we need to know the value of r.

Statement I is sufficient: 2 r = 32 So r = 5

Statement II is insufficient: It is a quadratic equation and It has two roots(r = 5 and r = -1) So not sufficient,