GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 10:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A pizza can be assembled from given choices, with customer’s preferenc

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

29 May 2018, 01:48
00:00

Difficulty:

75% (hard)

Question Stats:

50% (02:09) correct 50% (02:03) wrong based on 112 sessions

### HideShow timer Statistics

A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

A. 3
B. 9
C. 12
D. 36
E. 60

To solve question 3: P&C Practice Question 3

Related Articles:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions
Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

All Articles: Must Read Articles and Practice Questions to score Q51 !!!!

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3373
Location: India
GPA: 3.12
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

29 May 2018, 05:59
EgmatQuantExpert wrote:
A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

A. 3
B. 9
C. 12
D. 36
E. 60

EgmatQuantExpert - Is there a mistake in the question stem?
_________________
You've got what it takes, but it will take everything you've got
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

29 May 2018, 06:02
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3373
Location: India
GPA: 3.12
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

29 May 2018, 06:08
1
EgmatQuantExpert wrote:
A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

A. 3
B. 9
C. 12
D. 36
E. 60

The highlighted portion - I'm not so sure, but the meaning is not clear.
_________________
You've got what it takes, but it will take everything you've got
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

29 May 2018, 06:26
EgmatQuantExpert wrote:
A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

pushpitkc wrote:
The highlighted portion - I'm not so sure, but the meaning is not clear.

This indicates while making a choice, a customer may choose one of the types of toppings and/or one of the types of cheese. However he may also choose not to include any toppings or cheese as his choice.
Hope this clears.
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2888
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

31 May 2018, 01:52

Solution

Given:
• Number of varieties for
o Pizza crust = 3
o Toppings = 4
o Cheese = 3
• One have the choice of not choosing either of toppings or cheese

To find:
• Number of ways pizza can be customized

Approach and Working:
There are 4 possible cases:
• Choice of only crust, which can be done in $$^3C_1$$ = 3 ways
• Choice of crust and toppings, which can be done in $$^3C_1 * ^4C_1$$ = 3 * 4 = 12 ways
• Choice of crust and cheese, which can be done in $$^3C_1 * ^3C_1$$ = 3 * 3 = 9 ways
• Choice of crust, toppings, and cheese, which can be done in $$^3C_1 * ^4C_1 * ^3C_1$$ = 3 * 4 * 3 =36 ways
Therefore, the total number of ways pizza can be customized = 3 + 12 + 9 + 36 = 60 ways

Hence, the correct answer is option E.

_________________
Intern
Joined: 10 Oct 2017
Posts: 16
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

01 Jun 2018, 07:02
2
we can also try one more method.

Since we have an option of choosing (not choosing ) any cheese or topping.We can take this as extra option.

eg. now no. of toppings =5 (including the no choice option)
now of types of cheese=4(including the no choice option)

so, the total ways=3x5x4= 60
Manager
Joined: 11 Dec 2013
Posts: 120
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

11 Jan 2019, 22:10
Hi,

has the choice of not choosing either of toppings or cheese?

has the choice of not choosing toppings OR not choosing cheese .
Hence he needs to choose one of those .

Choice of crust and toppings = 3*4 = 12 ways
Choice of crust and cheese = 3*3 = 9 ways
Choice of crust, toppings, and cheese = 3*4*3 = 36 ways

_________________
Intern
Joined: 10 Feb 2017
Posts: 43
Location: India
Schools: Rotman '20
GMAT 1: 710 Q49 V37
GPA: 4
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

12 May 2019, 03:39
Number of varieties for
Pizza crust = 3
Toppings = 4
Cheese = 3
One have the choice of not choosing either of toppings or cheese
SO 1 VERITY OF CRUST WITH 1 VERITY OF TOPPINGS WILL HAVE 4 CHOICES(3 CHEESE AND 1 ADDED BKZ SOMEONE CAN EVEN CHOOSE NO CHEESE).
SIMILARLY 1 VERITY OF CRUST WITH 4 VERITY OF TOPPINGS WILL HAVE 20 CHOICES(5*4).5 BKZ SOMEONE CAN EVEN CHOOSE NO TOPPINGS ATALL.
BUT SINCE CRUST IS MANDATORY,TOTAL COMBINATIONS POSSIBLE=3*5*4=60
OA-E
Intern
Joined: 28 Jan 2017
Posts: 25
WE: Consulting (Computer Software)
Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

### Show Tags

25 May 2019, 06:40
EgmatQuantExpert wrote:

Solution

Given:
• Number of varieties for
o Pizza crust = 3
o Toppings = 4
o Cheese = 3
• One have the choice of not choosing either of toppings or cheese

To find:
• Number of ways pizza can be customized

Approach and Working:
There are 4 possible cases:
• Choice of only crust, which can be done in $$^3C_1$$ = 3 ways
• Choice of crust and toppings, which can be done in $$^3C_1 * ^4C_1$$ = 3 * 4 = 12 ways
• Choice of crust and cheese, which can be done in $$^3C_1 * ^3C_1$$ = 3 * 3 = 9 ways
• Choice of crust, toppings, and cheese, which can be done in $$^3C_1 * ^4C_1 * ^3C_1$$ = 3 * 4 * 3 =36 ways
Therefore, the total number of ways pizza can be customized = 3 + 12 + 9 + 36 = 60 ways

Hence, the correct answer is option E.

Hi,
I dont understand the 36 ways concept. why we are taking all the variants here?
Re: A pizza can be assembled from given choices, with customer’s preferenc   [#permalink] 25 May 2019, 06:40
Display posts from previous: Sort by