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# At a certain pizza parlor, the diameter of a large pizza is

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Magoosh GMAT Instructor
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At a certain pizza parlor, the diameter of a large pizza is [#permalink]

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10 Oct 2012, 11:04
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25% (medium)

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67% (07:04) correct 33% (01:03) wrong based on 278 sessions

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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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Re: At a certain pizza parlor, the diameter [#permalink]

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10 Oct 2012, 11:18
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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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Re: At a certain pizza parlor, the diameter [#permalink]

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10 Oct 2012, 11:38
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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]

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23 Nov 2013, 02:01
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Re: At a certain pizza parlor, the diameter of a large pizza is [#permalink]

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13 Dec 2013, 10:45
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?

If A = pi (r)^2 the A = pi (1/2d) ^2
Area (small) = pi (1/2d)^2
Area (small) = pi (1/4d)

Area (large) = pi (1/2*1.4d)^2
Area (large) = pi (1/2*7/5d)^2
Area (large) = pi (49/100d)

So, the radius of the large pizza is roughly 50% larger than the smaller pizza. If we plug in a number for d we can see the difference in sizes.
Area (small) = pi (1/4d)
Area (small) = pi (1/4 * 36)
Area (small) = pi(9)

Area (large) = pi (49/100d)
Area (large) = pi (49/100 * 36)
Area (large) = pi(18)

Therefore the area of the larger pizza is approximately 100% greater.

E

(A) 20%
(B) 40%
(C) 64%
(D) 80%
(E) 96%
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At a certain pizza parlor, the diameter of a large pizza is [#permalink]

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25 Apr 2014, 04:00
Let small pizza diameter = 100

Large pizza diameter would be = 140

Area of Circle $$= \pi * (\frac{d}{2})^2$$

$$= \frac{\pi}{4} * d^2$$

In the above, only variable is the diameter

$$100^2 = 10000$$

$$140^2 = 19600$$

Difference = 9600 or 96%

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Last edited by PareshGmat on 28 Jul 2014, 02:11, edited 1 time in total.
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At a certain pizza parlor, the diameter of a large pizza is [#permalink]

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28 Jul 2014, 01:29
We need the areas of the pizzas. We know: area (of circle)=r²*pi. 2r =d.

Now pick smart numbers:

diameter of small pizza: 10, then diameter of big pizza: 14

then: area small pizza: 25pi, area of big pizza = 49pi

Hence percent increase 49/25 = 1.96 = 96 % bigger.
At a certain pizza parlor, the diameter of a large pizza is   [#permalink] 28 Jul 2014, 01:29
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