Solutions

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Question

A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?


 

Option A:

5/12

Option B:

2/5

Option C:

1/2

Option D:

3/4

Option E:

5/6

Difficulty Level

Medium

Solution

Option C is the correct answer.


Option Analysis

Area of circle=πr^2=π10^2 ≈ 314 (d=20 –> r=10);

Area of square= (24)^2=576;

Area of circle/ area of square=314/576=157/288.

Now this fraction is obviously between 1/2 and 3/4 –> 1/2=144/288 and 3/4=216/288 — > 157 is closer to 144 than to 216.