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

4

This post was BOOKMARKED

00:00

A

B

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E

Difficulty:

75% (hard)

Question Stats:

50% (03:11) correct
50% (01:58) wrong based on 144 sessions

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

Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink]
27 Feb 2013, 05:17

1

This post received KUDOS

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.

Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink]
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

Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink]
23 Sep 2014, 04:38

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Marty's Pizza Shop guarantees that their pizzas all have a [#permalink]
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) _________________

Feel free to message if you have any questions :D

Last edited by TehMoUsE on 23 Sep 2014, 05:26, edited 1 time in total.

Re: Marty's Pizza Shop guarantees that their pizzas all have a [#permalink]
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. _________________

For my Cambridge essay I have to write down by short and long term career objectives as a part of the personal statement. Easy enough I said, done it...