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# There are two circle-shaped pizzas. The diameter of the smaller pizza

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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There are two circle-shaped pizzas. The diameter of the smaller pizza [#permalink]

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16 Jun 2016, 19:35
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Difficulty:

25% (medium)

Question Stats:

72% (01:05) correct 28% (01:16) wrong based on 78 sessions

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There are two circle-shaped pizzas. The diameter of the smaller pizza is 10 and the larger pizza’s area is 2 times of the smaller pizza’s area, what is the diameter of the larger pizza, in whole number?
A. 12
B. 15
C. 18
D. 20
E. 25

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

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Joined: 19 Dec 2015
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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza [#permalink]

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16 Jun 2016, 20:28
Let the radius of the small pizza be r, and the radius of the bigger pizza be R. Given $$pi.r^2$$ = $$pi.R^2$$. Thus R ~ 1.41r. Therefore D = 1.41d as well. = 1.41*10 = 14.10. The nearest whole number from the answer choices is 15. Hence B.
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Joined: 18 Jan 2010
Posts: 256
Re: There are two circle-shaped pizzas. The diameter of the smaller pizza [#permalink]

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16 Jun 2016, 21:30
MathRevolution wrote:
There are two circle-shaped pizzas. The diameter of the smaller pizza is 10 and the larger pizza’s area is 2 times of the smaller pizza’s area, what is the diameter of the larger pizza, in whole number?
A. 12
B. 15
C. 18
D. 20
E. 25

*An answer will be posted in 2 days.

Area of smaller pizza = ($$\pi$$$$10^2$$)/ 4, where 10 is the dia of smaller circle.

Area of bigger pizza = twice of area of smaller pizza = ($$\pi$$$$10^2$$)/ 2

if r is the radius of bigger pizza.

$$\pi$$$$r^2$$ = ($$\pi$$$$10^2$$)/ 2

$$r^2$$ = 50

r = $$\sqrt{50}$$
diameter = 2r = 10$$\sqrt{2}$$

dia = 14.1416.

nearest value should have been 14. It is not given. So we will choose 15.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4863
GPA: 3.82
Re: There are two circle-shaped pizzas. The diameter of the smaller pizza [#permalink]

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19 Jun 2016, 16:48
Expert's post
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Since √(proportion of area) = proportion of length. If the proportion of area is 2, then we have √2. Hence, the proportion of length becomes approximately 1.5. So, from 10*1.5=15. Thus, the correct answer is B.
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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza [#permalink]

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14 Aug 2017, 00:38
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Re: There are two circle-shaped pizzas. The diameter of the smaller pizza   [#permalink] 14 Aug 2017, 00:38
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