If circle A has 3 times the area of circle B, and circle B has one-six

Question

If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

A.  \frac{\pi}{12}

B.  \frac{\pi}{6}

C.  \frac{\pi}{2}

D.  \frac{2}{\pi}

E.  \sqrt {12\pi}

gmatophobia · Answer

Let the side of the square = s

Area of circle inscribed inside a square = \pi * (\frac{s}{2})^2  == \pi * \frac{s^2}{4}

Area of circle B =  \frac{s^2}{6}

Area of circle A =  \frac{s^2}{2}

Required Ratio =  \frac{\pi}{2}

Option C

SaquibHGMATWhiz · Answer

Solution: Let us take a few variables: r_1= radius of circle A, r_2= radius of circle B, a= side of square WXYZ WXYZ.png Area of circle inscribed inside square WXYZ = \pi (\frac{a}{2})^2 We are asked the ratio of area of a circle inscribed within WXYZ to that of the area of circle A i.e., the value of \frac{\pi (\frac{a}{2})^2}{\pi (r_1)^2}=\frac{a^2}{4(r_1)^2} This means we need the relation between a^2 and (r_1)^2 to get our answer According to the question, circle A has 3 times the area of circle B which means \pi (r_1)^2=3\pi (r_2)^2 OR (r_2)^2=\frac{(r_1)^2}{3} Secondly, we are given circle B has one-sixth of the area of square WXYZ which means \pi (r_2)^2=\frac{1}{6}a^2 ⇒\pi \frac{(r_1)^2}{3}=\frac{1}{6}a^2 ⇒\frac{a^2}{(r_1)^2}=2\pi We need the value of \frac{a^2}{4(r_1)^2}=\frac{2\pi}{4}=\frac{\pi}{2} Hence the right answer is Option C

bellbell · Answer

Let's say Square S has side a => radius of the circle C inscribed = 1/2a
The area of each one shall be as below:
A = πr^2
B = 1/3πr^2
S = 6*1.3πr^2 = 2πr^2 = a^2
C = (1/2a)^2*π = 1/2π*πr^2

=> C/A = (1/2π*πr^2)/(πr^2) = 1/2π = π/2

If circle A has 3 times the area of circle B, and circle B has one-six

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If circle A has 3 times the area of circle B, and circle B has one-six

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards