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If each of the 4 circles above has radius 1, what

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If each of the 4 circles above has radius 1, what

by Brent@GMATPrepNow » Tue May 29, 2018 5:22 am

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If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€

Answer: D
Difficulty level: 700+
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by GMATGuruNY » Tue May 29, 2018 5:57 am
Brent@GMATPrepNow wrote:Image

If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€

Image

Area of the blue square above = s² = 2² = 4.
Area of each circle = πr² = π(1²) = π.
Each unshaded portion in the blue square constitutes 1/4 of a circle.
Thus, the 4 unshaded portions combined constitute one full circle.
Shaded portion = (blue square) - (one full circle) = 4 - π.

The correct answer is D.
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by Brent@GMATPrepNow » Thu May 31, 2018 5:29 am
Brent@GMATPrepNow wrote:Image

If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 - π/4
B) 2 - π/4
C) 2 - π/2
D) 4 - π
E) 4 - 2Ï€

Answer: D
Difficulty level: 700+
Source: www.gmatprepnow.com
Here's a different approach:

Let's place a square around just one of the circles
Image


Notice that the shaded area IN the square represents 1/4 of the TOTAL shaded area in the diagram.
Image


This means that the shaded area in THIS diagram will be the same as the TOTAL shaded area in the ORIGINAL diagram.
Image


So, let's determine the area of the shaded area in the diagram below.
Image

Each side of the square has length 2, so the area of the SQUARE = (2)(2) = 4

The circle has radius 1.
So, the area of the CIRCLE = π(radius)² = π(1)² = π

So, the area of the SHADED region = 4 - π

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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