Author 
Message 
TAGS:

Hide Tags

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]
Show Tags
01 Nov 2013, 18:34
Question Stats:
91% (00:47) correct 9% (00:09) wrong based on 40 sessions
HideShow timer Statistics
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?



Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 68

Re: Mario's Pizza has two choices of crust: deep dish and thin
[#permalink]
Show Tags
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.



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]
Show Tags
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]
Show Tags
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]
Show Tags
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]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 60480

Re: Mario's Pizza has two choices of crust: deep dish and thin
[#permalink]
Show Tags
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.
_________________



Intern
Joined: 17 May 2015
Posts: 32

Re: Mario's Pizza has two choices of crust: deep dish and thin
[#permalink]
Show Tags
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]
Show Tags
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]
Show Tags
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.



NonHuman User
Joined: 09 Sep 2013
Posts: 13976

Re: Mario's Pizza has two choices of crust: deep dish and thin
[#permalink]
Show Tags
23 Nov 2019, 13:32
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




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






