Solutions
Get detailed explanations to advanced GMAT questions.
Question
What is the circumference of circular region R?
I. The area of R is 36 pi.
II. The area of a square region inscribed in R is 72.
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 D is the correct answer.
Option Analysis
We need to find circumference=2*pi*R or We need to find “R”
Statement I is sufficient: Area=pi*R*R=36pi…… so you can find R. So sufficient.
Statement II is sufficient: Area of square region in circle=72. So sufficient.
Diagonal of square will be diameter because angle drawn from 2 end-points of a diameter make 90 degrees angle on the circle. Since diagonal of square=2R. We can find side of square and hence area of square in terms of R. That means you can find R. So sufficient.
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