## Simple one :)

##### This topic has expert replies
Legendary Member
Posts: 1556
Joined: 14 Aug 2012
Thanked: 448 times
Followed by:34 members
GMAT Score:650

### Simple one :)

by theCodeToGMAT » Sat Sep 28, 2013 4:48 am
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}
R A H U L

Legendary Member
Posts: 643
Joined: 14 Aug 2013
Thanked: 48 times
Followed by:7 members
by vinay1983 » Sat Sep 28, 2013 5:35 am
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}
Is it 16? 12 with the cheese and and stuff and the regular 4
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!

Legendary Member
Posts: 1556
Joined: 14 Aug 2012
Thanked: 448 times
Followed by:34 members
GMAT Score:650
by theCodeToGMAT » Sat Sep 28, 2013 5:37 am
Yes.. correct..
R A H U L

### GMAT/MBA Expert

GMAT Instructor
Posts: 15965
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770
by [email protected] » Sat Sep 28, 2013 6:39 am
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
Take the task of building a pizza and break it into stages.

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

Brent Hanneson - Creator of GMATPrepNow.com

### GMAT/MBA Expert

GMAT Instructor
Posts: 15965
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770
by [email protected] » Sat Sep 28, 2013 6:50 am
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}
Since the 5 answer choices are all relatively small, we can also consider listing all of the possible options as a viable approach.

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

### GMAT/MBA Expert

Elite Legendary Member
Posts: 10392
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:510 members
GMAT Score:800
by [email protected] » Sat Sep 28, 2013 12:01 pm
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
Contact Rich at [email protected]

Legendary Member
Posts: 518
Joined: 12 May 2015
Thanked: 10 times
by nikhilgmat31 » Tue Oct 06, 2015 11:33 pm
[email protected] wrote:
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
Take the task of building a pizza and break it into stages.

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

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
by theCEO » Wed Oct 07, 2015 2:13 am
nikhilgmat31 wrote:
[email protected] wrote:
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
Take the task of building a pizza and break it into stages.

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

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
There are actually 4 options: Add extra cheese, mushrooms, both to any kind of pizza or add no toppings (cheese or muchroom)

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

Elite Legendary Member
Posts: 10392
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:510 members
GMAT Score:800
by [email protected] » Wed Oct 07, 2015 9:05 am
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

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]

Newbie | Next Rank: 10 Posts
Posts: 3
Joined: 06 Oct 2015
by patco » Wed Oct 07, 2015 1:28 pm
vinay1983 wrote:
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}
Is it 16? 12 with the cheese and and stuff and the regular 4
At first glance I would say just 12.. But, you gave the right answer extremely fast and with a logic!
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
by nikhilgmat31 » Wed Oct 07, 2015 9:04 pm
Thanks Rich, I missed the option of No Toppings.

• Page 1 of 1