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Marty's Pizza Shop guarantees that their pizzas all have a

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New post Updated on: 27 Feb 2013, 05:19
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Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches

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Originally posted by emmak on 27 Feb 2013, 04:14.
Last edited by Bunuel on 27 Feb 2013, 05:19, edited 1 time in total.
Edited the question.
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New post 27 Feb 2013, 06:17
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emmak wrote:
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches


The area of 16 inches pizza is \(\pi{R^2}=8^2\pi=64\pi\).

The minimum area covered with toppings is \(\frac{3}{4}*64\pi=48\pi\) --> the radius of the toppings is \(\pi{r^2}=48\pi\) --> \(r=4\sqrt{3}\approx{6.9}\).

The maximum width for the crust possible = R - r = 8 - 6.9 = 1.1 inches.

Answer: B.
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New post 03 Mar 2013, 06:50
Hmmm not an official question and the wording is tough on this
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Re: Marty's Pizza Shop guarantees that their pizzas all have a  [#permalink]

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New post 03 Mar 2013, 21:07
emmak wrote:
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches


Total Area = 8 * 8 * pi
Radius = 64 pi

Surface = .75 * 64 * pi = 48 pi
Radius of surface = 4 sqrt (3) ~ 6.8

Radius width = 8 - 6.8 = 1.2

Answer: B
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New post Updated on: 23 Sep 2014, 06:26
Bunuel wrote:
emmak wrote:
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches


The area of 16 inches pizza is \(\pi{R^2}=8^2\pi=64\pi\).

The minimum area covered with toppings is \(\frac{3}{4}*64\pi=48\pi\) --> the radius of the toppings is \(\pi{r^2}=48\pi\) --> \(r=4\sqrt{3}\approx\) 6,9

The maximum width for the crust possible = R - r = 8 - 6.9 = 1.1 inches.

Answer: B.


\(r=4\sqrt{3}=6.9282....\).

The maximum width for the crust possible = R - r = 8 - 6.9282... = 1.0717.... inches. -----> 1,1 width would make the surface area covered with topping less than 75%

Answer: A

I know this might be picky, but shouldn't OA be A ?
Does GMAT give these possible answers where rounding errors become very important
Please fill me in case Im missing something (which I probably do)
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Originally posted by TehMoUsE on 23 Sep 2014, 06:20.
Last edited by TehMoUsE on 23 Sep 2014, 06:26, edited 1 time in total.
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New post 23 Sep 2014, 06:25
TehMoUsE wrote:
Bunuel wrote:
emmak wrote:
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches


The area of 16 inches pizza is \(\pi{R^2}=8^2\pi=64\pi\).

The minimum area covered with toppings is \(\frac{3}{4}*64\pi=48\pi\) --> the radius of the toppings is \(\pi{r^2}=48\pi\) --> \(r=4\sqrt{3}\approx{6.9}\).

The maximum width for the crust possible = R - r = 8 - 6.9 = 1.1 inches.

Answer: B.


\(r=4\sqrt{3}\={6.9282....}\).

The maximum width for the crust possible = R - r = 8 - 6.9282... = 1.0717.... inches. -----> 1,1 width would make the surface area covered with topping less than 75%

Answer: A

I know this might be picky, but shouldn't OA be A ?


The approximate maximum is 1.1 inches.
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New post 23 Sep 2014, 06:32
Bunuel wrote:
The approximate maximum is 1.1 inches.


I understand that, but the question doesn't say anything about approximations.

Is it silently implied in GMAT that you round up to the closest number, even tho it would give you the "wrong" answer?
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New post 23 Sep 2014, 06:37
TehMoUsE wrote:
Bunuel wrote:
The approximate maximum is 1.1 inches.


I understand that, but the question doesn't say anything about approximations.

Is it silently implied in GMAT that you round up to the closest number, even tho it would give you the "wrong" answer?


Word "approximate" is missing there. It should be "what is the approximate maximum width you can expect to see for the crust?"
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Re: Marty's Pizza Shop guarantees that their pizzas all have a  [#permalink]

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New post 23 Sep 2014, 07:31
Hi Bunuel,

I am not able to find the solution with this method.

x be the width of the surrounding

pi (8-x)^2/pi(8)^2 = 3/4

does not lead to the answer..I am not able to find whats wrong in this approach.

Please help.

Regards,
Ravi
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New post 24 Sep 2014, 05:29
email2vm wrote:
Hi Bunuel,

I am not able to find the solution with this method.

x be the width of the surrounding

pi (8-x)^2/pi(8)^2 = 3/4

does not lead to the answer..I am not able to find whats wrong in this approach.

Please help.

Regards,
Ravi


There is nothing wrong with this approach.

\(\frac{\pi (8-x)^2}{\pi(8)^2} = \frac{3}{4}\) --> \((8-x)^2=48\) --> \(8-x=4\sqrt{3}=6.9\) --> \(x=8-6.9=1.1\).
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Re: Marty's Pizza Shop guarantees that their pizzas all have a  [#permalink]

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New post 31 May 2015, 11:01
Bunuel wrote:
TehMoUsE wrote:
Bunuel wrote:
The approximate maximum is 1.1 inches.


I understand that, but the question doesn't say anything about approximations.

Is it silently implied in GMAT that you round up to the closest number, even tho it would give you the "wrong" answer?


Word "approximate" is missing there. It should be "what is the approximate maximum width you can expect to see for the crust?"


I think the keyword here is "at least" so, if 75% calculation comes to 1.08 we have no choice but to round up and select the closest, which in this case is 1.10 and not 1.06, which will breach the requirement of "at least 75%".. Lemme know your views. Thanks.
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Re: Marty's Pizza Shop guarantees that their pizzas all have a  [#permalink]

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New post 07 Mar 2019, 07:54
emmak wrote:
Marty's Pizza Shop guarantees that their pizzas all have at least 75% of the surface area covered with toppings, with a crust of uniform width surrounding them. If you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust?

A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches


Since the diameter is 16 inches, the radius is 8 inches, and the surface area is 8^2(π) = 64π. Since the toppings covers at least 75% of the surface area, the toppings covers at least 0.75 x 64π = 48π. Therefore, the radius of the toppings’ surface area is √48 ≈ 6.9 inches. Therefore, the maximum width of the crust is approximately 8 - 6.9 = 1.1 inches.

Answer: B
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Re: Marty's Pizza Shop guarantees that their pizzas all have a   [#permalink] 07 Mar 2019, 07:54
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