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# The area of a circle with radius a is less than the area of a square

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Math Expert
Joined: 02 Sep 2009
Posts: 60687
The area of a circle with radius a is less than the area of a square  [#permalink]

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10 Dec 2019, 01:55
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Difficulty:

55% (hard)

Question Stats:

50% (02:20) correct 50% (02:20) wrong based on 22 sessions

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The area of a circle with radius $$a$$ is less than the area of a square with sides of length $$ka$$. Which of the following could be the value of k?

I. $$\frac{5}{3}$$

II. $$\frac{6}{3}$$

III. $$\frac{7}{3}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

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Joined: 16 Feb 2015
Posts: 268
Location: United States
Concentration: Finance, Operations
Re: The area of a circle with radius a is less than the area of a square  [#permalink]

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10 Dec 2019, 04:14
1
Bunuel wrote:
The area of a circle with radius $$a$$ is less than the area of a square with sides of length $$ka$$. Which of the following could be the value of k?

I. $$\frac{5}{3}$$

II. $$\frac{6}{3}$$

III. $$\frac{7}{3}$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Explanation:
K^2 > 3.14
As Area of a circle is (3.14)*a^2
Area of Square: K^2 x a^2
Given the area of square is more than the area of a circle
Only with Option II & III are possible.
In Option I, It is less than the value of 3.14

IMO D
Re: The area of a circle with radius a is less than the area of a square   [#permalink] 10 Dec 2019, 04:14
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