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# Mario's Pizza has two choices of crust: deep dish and thin

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Manager
Joined: 11 Jan 2011
Posts: 57
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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01 Nov 2013, 18:34
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Question Stats:

91% (00:47) correct 9% (00:09) wrong based on 40 sessions

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Mario's Pizza has two choices of crust: deep dish and thin-and-crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers very pizza in extra-cheese as well as regular. If Linda's volleyball team decides to order a pizza with four toppings, how many different choices do the teammates have at Mario's Pizza?

My approach (with spoiler):

Total number of choices = 2 crust x 5 toppings x 2 cheese = 20
Vball team: 2 crust x 4 toppings x 2 cheese = 16 choices

I understand this approach is incorrect because instead of first saying choose 4 out of 5 toppings, it essentially eliminates a topping.

However, why would the correct approach, 2 crust x 5c4 toppings x 2 cheese, be the same as the "total" possibilities, 20? Is it just a coincidence that the numbers worked out this way in this problem?

OA = 20
Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 68
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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01 Nov 2013, 22:15
1
Yes, it is a coincidence that you arrived at the correct answer on this problem. It's unfortunate when that happens, because it's often hard to figure out why the approach is wrong.

Basically, your middle term (5 toppings) is appropriate for selecting 1 topping at a time out of 5 options.

Coincidentally, this parallels the correct approach of selecting 4 toppings at a time out of 5 options. With the latter, you effectively leave out 1 topping for each option, which has the effect of also giving you 5 different combinations.

But notice, having 5 different groupings of 4 toppings each (5c4) is very different from choosing 1 of 5 toppings at a time (5c1). They just happen to provide the same number of possible configurations.
Manager
Joined: 11 Jan 2011
Posts: 57
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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06 Nov 2013, 10:57
Thanks, that makes sense.
Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 68
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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06 Nov 2013, 21:12
NvrEvrGvUp wrote:
Thanks, that makes sense.

I'm glad the explanation helped. Keep at it!
Intern
Joined: 11 Aug 2013
Posts: 28
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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08 Nov 2013, 21:20
5x2x2 =20, this is a mgmat questions. The end is slightly different.
Intern
Joined: 17 May 2015
Posts: 32
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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15 Jun 2015, 04:10
1
need great help to correct my steps/understanding:
I need to choose one of crust with 4 toppings.
so I need to choose 1 from 2 and 4 toppings from 5:
my work is as follows:
2/1! multiply 5x4x3x2 / 4!
= 2 / 1 x 5x4x3x2/4x3x2x1
= 2 x 5
= 10 choices
why my answer is wrong, need great help
is cheese and regular is also part of the equation.
Many thanks
Math Expert
Joined: 02 Sep 2009
Posts: 60480
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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15 Jun 2015, 04:51
2
1
apple08 wrote:
need great help to correct my steps/understanding:
I need to choose one of crust with 4 toppings.
so I need to choose 1 from 2 and 4 toppings from 5:
my work is as follows:
2/1! multiply 5x4x3x2 / 4!
= 2 / 1 x 5x4x3x2/4x3x2x1
= 2 x 5
= 10 choices
why my answer is wrong, need great help
is cheese and regular is also part of the equation.
Many thanks

There is one more piece of information: Mario's offers very pizza in extra-cheese as well as regular.

Mario's Pizza has two choices of crust: deep dish and thin-and-crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers very pizza in extra-cheese as well as regular. If Linda's volleyball team decides to order a pizza with four toppings, how many different choices do the teammates have at Mario's Pizza?

Mario's Pizza:
2 choices of crust.
5 choices of toppings.
2 choices of cheese (extra-cheese or regular).

Linda decides to order a pizza with four toppings.

How many 4-topping pizzas are possible from 5? $$C^4_5=5$$. But the pizza can have 2 different crusts and two different cheese, therefore the final answer is 5*2*2 = 20.
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Intern
Joined: 17 May 2015
Posts: 32
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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17 Jun 2015, 00:03
Many thanks Bunuel really really appreciate it
Senior Manager
Joined: 15 Oct 2015
Posts: 297
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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15 Dec 2015, 04:57
Is this actually sub600? cos it's seems some users are as confused as I am. GMAT is really a foreign language tests.
was the level randomly assigned?
Senior Manager
Joined: 15 Oct 2015
Posts: 297
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)
Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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15 Dec 2015, 05:13
In the question there was mention of "crust". As I don't eat pizzas, and don't know the details of what constitute pizzas, I might need to get a lesson on pizza preparation.
but I guess from the problem, crust n toppings are stuffs for making pizzas. right? if you order a pizza with four toppings, how many choices do u have?
what happened to crust plz!
And finally, what does "finally... extra-cheese as well as regular" mean?
Thanks.
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Joined: 09 Sep 2013
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Re: Mario's Pizza has two choices of crust: deep dish and thin  [#permalink]

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23 Nov 2019, 13:32
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Re: Mario's Pizza has two choices of crust: deep dish and thin   [#permalink] 23 Nov 2019, 13:32
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