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A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,

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A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post Updated on: 12 Oct 2014, 02:43
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A university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?

(A) 4
(B) 8
(C) 12
(D) 16
(E) 32

Originally posted by jrymbei on 11 Oct 2014, 16:49.
Last edited by Bunuel on 12 Oct 2014, 02:43, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post 12 Oct 2014, 02:47
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jrymbei wrote:
A university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?

(A) 4
(B) 8
(C) 12
(D) 16
(E) 32


There are 4 flavors of pizza and each can be:
1. Without cheese and mushrooms;
2. With cheese;
3. With mushrooms;
4. With cheese and mushrooms.

So, the total number of pizza varieties is 4*4 = 16.

Answer: D.
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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post 12 Oct 2014, 02:53
4 flavours * 4 choices = 4C1*4C1 = 4*4=16

Note: The question says in that among the options of cheese, mushroom or both, they have the choice but not the obligation of picking the option. So we have a 4 options - cheese, mushroom, both or *none*.
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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post 19 Nov 2014, 07:43
In this case, if it becomes obligatory to add either cheese, mushroom, or both.
Then the "none" varieties will be 0.

Total varieties would then be 12.
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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post 13 Feb 2018, 22:45
Hi All,

From the answer choices, we know that the number of total possibilities is limited, so we can 'map them' all out:

4 types of pizza and 4 options per pizza:

Pepperoni - as is, extra cheese, mushrooms, BOTH cheese/mushrooms = 4 options
Chicken - as is, extra cheese, mushrooms, BOTH cheese/mushrooms = 4 options
Hawaiian - as is, extra cheese, mushrooms, BOTH cheese/mushrooms = 4 options
Vegetarian - as is, extra cheese, mushrooms, BOTH cheese/mushrooms = 4 options

Total = 4+4+4+4 = 16 varieties

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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken,  [#permalink]

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New post 15 Feb 2018, 11:04
jrymbei wrote:
A university cafeteria offers 4 flavors of pizza - pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?

(A) 4
(B) 8
(C) 12
(D) 16
(E) 32


We are given 4 flavors for pizza and there are 4 options for each flavor: no toppings, cheese-only, mushrooms-only, and both toppings. Thus, we have 4 x 4 = 16 different pizzas possible.

Answer: D
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Re: A university cafeteria offers 4 flavors of pizza – pepperoni, chicken, &nbs [#permalink] 15 Feb 2018, 11:04
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