What percent of the squares area is taken up by the circle?

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

What percent of the squares area is taken up by the circle?

by BTGmoderatorDC » Tue Apr 13, 2021 6:14 pm

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What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %

OA B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Apr 13, 2021 6:14 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: What percent of the squares area is taken up by the circle?

by Scott@TargetTestPrep » Mon Apr 26, 2021 6:42 am

BTGmoderatorDC wrote: ↑
Tue Apr 13, 2021 6:14 pm
Geometry_Q1_Image.jpg

What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %

OA B

Solution:

The area of the circle is πr^2 and the area of the square is (2r)^2 = 4r^2. Therefore, the area circle is πr^2 / (4r^2) x 100 = π/4 x 100 = 25π percent of the area of the square.

Alternate Solution:

The percent of the square’s area taken up by the circle is independent of the circle’s radius; thus we can immediately eliminate choices A, D, and E. It is impossible for an inscribed circle to take up more than 100% of the square; thus, we eliminate answer choice C as well (notice that 50 * π is greater than 100). The only remaining answer choice is B.

Answer: B

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