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.
Difficulty Level
MediumSolution
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,
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