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

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Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 27 Feb 2013, 03:14
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Feb 2013, 04:19, edited 1 time in total.
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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 27 Feb 2013, 05:17
Expert's post
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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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 03 Mar 2013, 05:50
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] New post 03 Mar 2013, 20:07
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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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 23 Sep 2014, 04:38
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Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 23 Sep 2014, 05:20
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)

Last edited by TehMoUsE on 23 Sep 2014, 05:26, edited 1 time in total.
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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 23 Sep 2014, 05:25
Expert's post
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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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 23 Sep 2014, 05:32
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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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 23 Sep 2014, 05:37
Expert's post
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] New post 23 Sep 2014, 06:31
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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Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink] New post 24 Sep 2014, 04:29
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Marty's Pizza Shop guarantees that their pizzas all have a   [#permalink] 24 Sep 2014, 04:29
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