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 :)
This topic has expert replies
 theCodeToGMAT
 Legendary Member
 Posts: 1556
 Joined: 14 Aug 2012
 Thanked: 448 times
 Followed by:34 members
 GMAT Score:650
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}
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
 theCodeToGMAT
 Legendary Member
 Posts: 1556
 Joined: 14 Aug 2012
 Thanked: 448 times
 Followed by:34 members
 GMAT Score:650
GMAT/MBA Expert
 Brent@GMATPrepNow
 GMAT Instructor
 Posts: 14456
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1262 members
 GMAT Score:770
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
Brent Hanneson  Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60Day Study Guide
Watch these video reviews of my course
And check out these free resources
Use my video course along with Beat The GMAT's free 60Day Study Guide
Watch these video reviews of my course
And check out these free resources
GMAT/MBA Expert
 Brent@GMATPrepNow
 GMAT Instructor
 Posts: 14456
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1262 members
 GMAT Score:770
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
Brent Hanneson  Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60Day Study Guide
Watch these video reviews of my course
And check out these free resources
Use my video course along with Beat The GMAT's free 60Day Study Guide
Watch these video reviews of my course
And check out these free resources
GMAT/MBA Expert
 Rich.C@EMPOWERgmat.com
 Elite Legendary Member
 Posts: 10346
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:503 members
 GMAT Score:800
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

 Legendary Member
 Posts: 518
 Joined: 12 May 2015
 Thanked: 10 times
Brent@GMATPrepNow 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

 Master  Next Rank: 500 Posts
 Posts: 363
 Joined: 17 Oct 2010
 Thanked: 115 times
 Followed by:3 members
There are actually 4 options: Add extra cheese, mushrooms, both to any kind of pizza or add no toppings (cheese or muchroom)nikhilgmat31 wrote:Brent@GMATPrepNow 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.
GMAT/MBA Expert
 Rich.C@EMPOWERgmat.com
 Elite Legendary Member
 Posts: 10346
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:503 members
 GMAT Score:800
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}
It's not so hard to raise and train a dog as long as you know what exactly to do... A good community to read some good dog training tips where you can learn a lot.

 Legendary Member
 Posts: 518
 Joined: 12 May 2015
 Thanked: 10 times