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At a certain pizza parlor, the diameter of a large pizza is
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10 Oct 2012, 10:04
Question Stats:
70% (01:41) correct 30% (01:44) wrong based on 344 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/scalefact ... decreases/
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Re: At a certain pizza parlor, the diameter
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10 Oct 2012, 10:18
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
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10 Oct 2012, 10:38
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/scalefact ... 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. Answer: E.
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Re: At a certain pizza parlor, the diameter of a large pizza is
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13 Dec 2013, 09:45
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
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Updated on: 28 Jul 2014, 01:11
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% Answer = E
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Originally posted by PareshGmat on 25 Apr 2014, 03:00.
Last edited by PareshGmat on 28 Jul 2014, 01:11, edited 1 time in total.



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At a certain pizza parlor, the diameter of a large pizza is
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28 Jul 2014, 00:29
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.



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Re: At a certain pizza parlor, the diameter of a large pizza is
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02 Feb 2018, 06:25
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/scalefact ... decreases/ \(40 + 40 + \frac{40*40}{100} = 96\), Answer will be (E)
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