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Manager
Joined: 11 Jan 2011
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GMAT 1: 680 Q44 V39 GMAT 2: 710 Q48 V40

Mario's Pizza has two choices of crust: deep dish and thin
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01 Nov 2013, 18:34
Question Stats:
91% (00:47) correct 9% (00:09) wrong based on 36 sessions
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Mario's Pizza has two choices of crust: deep dish and thinandcrispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers very pizza in extracheese 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?



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Re: Mario's Pizza has two choices of crust: deep dish and thin
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01 Nov 2013, 22:15
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.
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Re: Mario's Pizza has two choices of crust: deep dish and thin
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06 Nov 2013, 10:57
Thanks, that makes sense.



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Re: Mario's Pizza has two choices of crust: deep dish and thin
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06 Nov 2013, 21:12
NvrEvrGvUp wrote: Thanks, that makes sense. I'm glad the explanation helped. Keep at it!
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Re: Mario's Pizza has two choices of crust: deep dish and thin
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08 Nov 2013, 21:20
5x2x2 =20, this is a mgmat questions. The end is slightly different.



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Re: Mario's Pizza has two choices of crust: deep dish and thin
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15 Jun 2015, 04:10
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



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Re: Mario's Pizza has two choices of crust: deep dish and thin
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15 Jun 2015, 04:51
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 extracheese as well as regular. Mario's Pizza has two choices of crust: deep dish and thinandcrispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. Finally, Mario's offers very pizza in extracheese 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 (extracheese or regular). Linda decides to order a pizza with four toppings. How many 4topping 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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Re: Mario's Pizza has two choices of crust: deep dish and thin
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17 Jun 2015, 00:03
Many thanks Bunuel really really appreciate it



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



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Re: Mario's Pizza has two choices of crust: deep dish and thin
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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... extracheese as well as regular" mean? Pizza eating guys please explain. Thanks.



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