Solutions

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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

Medium

Solution

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.