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# If (d) denotes the area of a circle with diameter d, then

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If (d) denotes the area of a circle with diameter d, then [#permalink]  21 Dec 2008, 13:06
If (d) denotes the area of a circle with diameter d, then which of the following is equal to
(4)* (6) ?
(A) 10
(B) 12
(C) 24
(D) π ⋅ 12
(E) π ⋅ 24
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Re: defined function [#permalink]  21 Dec 2008, 14:15
mishak wrote:
If (d) denotes the area of a circle with diameter d, then which of the following is equal to
(4)* (6) ?
(A) 10
(B) 12
(C) 24
(D) π ⋅ 12
(E) π ⋅ 24

I don't think any of the answers are correct.
If (d) denotes the area of a circle with diameter d, then for (4) the radius of circle is 4/2 or 2, and the area of the circle with radius of 2 is 4pie
For (6) the radius of circle is 6/2 or 3, and the area of the circle with radius of 3 is 9pie
(4)*(6) would be 36(pie)^2, which I didn't find in any of the answer choices. Are you sure the question is correct?
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Re: defined function [#permalink]  21 Dec 2008, 14:47
there is explanation in the book

(4) * (6)= (4/2)^2 *pi * (6/2)^2 pi = 4pi * 9 pi = 36 pi^2

now

pi * (12) = pi * pi (12/2)^2 = pi^2 *6^2= 36 pi ^2

the last part I am trying to figure out
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Re: defined function [#permalink]  21 Dec 2008, 14:59
mishak wrote:
there is explanation in the book

(4) * (6)= (4/2)^2 *pi * (6/2)^2 pi = 4pi * 9 pi = 36 pi^2

now

pi * (12) = pi * pi (12/2)^2 = pi^2 *6^2= 36 pi ^2

the last part I am trying to figure out

I don't think I get the last part either. And I scored 51Q on the real GMAT. What source is this question from?
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Re: defined function [#permalink]  21 Dec 2008, 15:03
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Re: defined function [#permalink]  21 Dec 2008, 16:29
(12)*pi does not mean 12xpi. It means the area of a circle that has diameter 12. So the area of a circle with diameter 12 =6^2*pi, so (12)*pi = 36*pi^2.
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Senior Manager
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Re: defined function [#permalink]  21 Dec 2008, 18:24
highhopes wrote:
(12)*pi does not mean 12xpi. It means the area of a circle that has diameter 12. So the area of a circle with diameter 12 =6^2*pi, so (12)*pi = 36*pi^2.

I guess I can only think of it this way. If the answer is (12), then it will make more sense.
Re: defined function   [#permalink] 21 Dec 2008, 18:24
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