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

Question

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:
https://magoosh.com/gmat/2012/scale-fact ... decreases/

piyatiwari · Answer

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.

Bunuel · Answer

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.

WholeLottaLove · Answer

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%

PareshGmat · Answer

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

unceldolan · Answer

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.

Abhishek009 · Answer

40 + 40 + \frac{40*40}{100} = 96 , Answer will be (E)

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

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

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