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# At a certain pizza parlor, the diameter

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Kudos [?]: 586 [0], given: 14

At a certain pizza parlor, the diameter [#permalink]  10 Oct 2012, 11:04
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Question Stats:

84% (34:34) correct 15% (00:27) wrong based on 1 sessions
At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large?
(A) 20%
(B) 40%
(C) 64%
(D) 80%
(E) 96%

See a full discussion of the mathematical principles involved in this question, as well as a complete solution, at:
http://magoosh.com/gmat/2012/scale-fact ... decreases/
[Reveal] Spoiler: OA

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Mike McGarry
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Kudos [?]: 83 [1] , given: 46

Re: At a certain pizza parlor, the diameter [#permalink]  10 Oct 2012, 11:18
1
KUDOS
Let the pizzas be thin crust! Not considering height.

Small : diameter x, radius x/2, area (total amount of pizza) = pi * (x/2)^2
Large : diameter 1.4x, radius 1.4x/2, area (total amount of pizza) = pi * (1.4x/2)^2 = (1.4)^2 * area of small pizza = 1.96 * area of small pizza

So E is right.
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Kudos [?]: 9611 [1] , given: 829

Re: At a certain pizza parlor, the diameter [#permalink]  10 Oct 2012, 11:38
1
KUDOS
mikemcgarry wrote:
At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large?
(A) 20%
(B) 40%
(C) 64%
(D) 80%
(E) 96%

See a full discussion of the mathematical principles involved in this question, as well as a complete solution, at:
http://magoosh.com/gmat/2012/scale-fact ... decreases/

We need to find by what percent is the area of big pizza greater than the area of small pizza.

Since D (diameter) in the area formula is squared (area=\frac{\pi*d^2}{4}), then 40% increase in diameter, or increase 1.4 times, would be equivalent to 1.4^2=1.96 times increase in the area, which is the same as 96% increase.

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Re: At a certain pizza parlor, the diameter   [#permalink] 10 Oct 2012, 11:38
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