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by lukester » Sun Dec 19, 2010 6:07 am
I just did prep test on princeton and found this question hard to understand what I am supposed to do. The explaination didn't quite work out for me either. I was wondering if anyone can point me the right direction I should look at for this question?

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) π/12
B) π/6
C) π/2
D) 2/Ï€
E) √12π


OA: C
[spoiler][/spoiler]
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by ov25 » Sun Dec 19, 2010 6:16 am
C
side of wxyz, w so w^2
Circle B = 1/6w^2
Circle A = 3*1/6w = 1/2w^2
Circle C (inscribed in wxyz) = 1/2w^2*pi = pi^2/4w^2
so c:a = p^2/4w^2:1/2w^2 => pi/2
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by GMATGuruNY » Sun Dec 19, 2010 7:01 am
lukester wrote:I just did prep test on princeton and found this question hard to understand what I am supposed to do. The explaination didn't quite work out for me either. I was wondering if anyone can point me the right direction I should look at for this question?

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) π/12
B) π/6
C) π/2
D) 2/Ï€
E) √12π


OA: C
[spoiler][/spoiler]
We can plug in values that follow the conditions given in the problem.

Plug in area of WXYZ = 36.
Side = 6, so radius of inscribed circle = 3, and area of inscribed circle = π(3^2) = 9π.
Circle B = (1/6)(WXYZ) = (1/6)*36 = 6.
Circle A = 3*(Circle B) = 3*6 = 18.
Inscribed circle/Circle A = 9π/18 = π/2.

The correct answer is C.
Last edited by GMATGuruNY on Sun Dec 19, 2010 8:01 am, edited 1 time in total.
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by Rahul@gurome » Sun Dec 19, 2010 7:59 am
lukester wrote: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) π/12
B) π/6
C) π/2
D) 2/Ï€
E) √12π
The question gives us the following relations:
  • 1. Area of circle A = 3*(Area of circle B)
    2. Area of circle B = (Area of square WXYZ)/6
And asks for the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A.

Now side of square WXYZ = Diameter of the circle inscribed in it = a (Say)

Area of square WXYZ = a²
Area of inscribed circle = π(a/2)² = (π/4)*a² = (π/4)*(Area of square WXYZ)

Now replace the given information one by one,
Area of inscribed circle = (Ï€/4)*(Area of square WXYZ) = (Ï€/4)*(6*(Area of circle B)) = (Ï€/4)*(6*(Area of circle A)/3) = (Ï€/2)*(Area of circle A)

Therefore the required ratio = π/2

The correct answer is C.
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