A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
OA {B}
Simple one :)
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 theCodeToGMAT
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Is it 16? 12 with the cheese and and stuff and the regular 4theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
OA {B}
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 theCodeToGMAT
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Take the task of building a pizza and break it into stages.theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
Stage 1: Choose one of the flavors
There are 4 flavors of pizza (pepperoni, chicken, Hawaiian and vegetarian), so we can complete stage 1 in 4 ways
Stage 2: Choose whether to add extra cheese
We can either add extra cheese or not add extra cheese, so we can complete stage 2 in 2 ways.
Stage 3: Choose whether to add mushrooms
We can either add mushrooms or not mushrooms, so we can complete stage 3 in 2 ways.
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus build a pizza) in (4)(2)(2) ways ([spoiler]= 16 ways[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmatcounting?id=775
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Since the 5 answer choices are all relatively small, we can also consider listing all of the possible options as a viable approach.theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
OA {B}
P = pepperoni
C = chicken
H = hawaiian
V = vegetarian
E = extra cheese
M = mushrooms
All possible pizzas
 P
 C
 H
 V
 PE
 CE
 HE
 VE
 PM
 CM
 HM
 VME
 PME
 CME
 HME
 VME
Total = [spoiler]16 = B[/spoiler]
Cheers,
Brent
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Hi All,
This question is more about organization and thoroughness than math skills. The various explanations present different way to organize the work, so I'll add one more option:
With 4 types of pizzas (pepperoni, chicken, Hawaiian and vegetarian) and 4 options (AS IS, extra cheese, extra mushrooms, BOTH extra cheese and mushrooms).
4 x 4 = 16
GMAT assassins aren't born, they're made,
Rich
This question is more about organization and thoroughness than math skills. The various explanations present different way to organize the work, so I'll add one more option:
With 4 types of pizzas (pepperoni, chicken, Hawaiian and vegetarian) and 4 options (AS IS, extra cheese, extra mushrooms, BOTH extra cheese and mushrooms).
4 x 4 = 16
GMAT assassins aren't born, they're made,
Rich

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[email protected] wrote:Take the task of building a pizza and break it into stages.theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
Stage 1: Choose one of the flavors
There are 4 flavors of pizza (pepperoni, chicken, Hawaiian and vegetarian), so we can complete stage 1 in 4 ways
Stage 2: Choose whether to add extra cheese
We can either add extra cheese or not add extra cheese, so we can complete stage 2 in 2 ways.
Stage 3: Choose whether to add mushrooms
We can either add mushrooms or not mushrooms, so we can complete stage 3 in 2 ways.
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus build a pizza) in (4)(2)(2) ways ([spoiler]= 16 ways[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmatcounting?id=775
Hi Brent
I think Answer should be 12
since 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian.
3 Options Add extra cheese, mushrooms, or both to any kind of pizza,
Total Options  4 * 3 = 12

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There are actually 4 options: Add extra cheese, mushrooms, both to any kind of pizza or add no toppings (cheese or muchroom)nikhilgmat31 wrote:[email protected] wrote:Take the task of building a pizza and break it into stages.theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
Stage 1: Choose one of the flavors
There are 4 flavors of pizza (pepperoni, chicken, Hawaiian and vegetarian), so we can complete stage 1 in 4 ways
Stage 2: Choose whether to add extra cheese
We can either add extra cheese or not add extra cheese, so we can complete stage 2 in 2 ways.
Stage 3: Choose whether to add mushrooms
We can either add mushrooms or not mushrooms, so we can complete stage 3 in 2 ways.
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus build a pizza) in (4)(2)(2) ways ([spoiler]= 16 ways[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmatcounting?id=775
Hi Brent
I think Answer should be 12
since 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian.
3 Options Add extra cheese, mushrooms, or both to any kind of pizza,
Total Options  4 * 3 = 12
The question states that the customer has the option to add the toppings. This means that he does not have to add any toppings
Last edited by theCEO on Wed Oct 07, 2015 2:18 am, edited 1 time in total.
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Hi nikhilgmat31,
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
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
At first glance I would say just 12.. But, you gave the right answer extremely fast and with a logic!vinay1983 wrote:Is it 16? 12 with the cheese and and stuff and the regular 4theCodeToGMAT wrote:A university cafeteria offers 4 flavors of pizza  pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option to add extra cheese, mushrooms, or both to any kind of pizza, how many different pizza varieties are available?
a) 12
b) 16
c) 8
d) 20
c) 10
OA {B}
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