GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 13 Jul 2020, 07:45

### 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

# Sam has 8 trousers and 12 shirts. 2 particular trousers can never be

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Jan 2018
Posts: 6
Location: India
GPA: 4
WE: Supply Chain Management (Transportation)
Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

### Show Tags

01 Apr 2019, 04:43
8
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:09) correct 42% (03:00) wrong based on 36 sessions

### HideShow timer Statistics

Sam has 8 trousers and 12 shirts. 2 particular trousers can never be worn with any one of 3 particular shirts, and 2 other particular trousers must be worn with any one of 4 other particular shirts. In how many ways can Sam match up a trouser with a shirt?

(A) 94
(B) 88
(C) 66
(D) 82
(E) 74

Source:- EduShastra Class Sheet.
Manager
Joined: 21 Feb 2019
Posts: 123
Location: Italy
Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

### Show Tags

01 Apr 2019, 06:37
2
$$2*9 = 18$$, where 9 = 12 shirts - 3 particular shirts that can never be worn
$$2*4 = 8$$
$$4*12 = 48$$, trousers without dress restrictions.

Sum all cases: $$74$$. Hence, E.
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1998
Location: India
Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

### Show Tags

02 Apr 2019, 03:15
As two trousers can't be worn by 3 particular shirts, hence they can be worn by rest 9 shirts. Combination possible= 2*9
2 trousers must be worn with 4 particular shirts, combinations possible= 2*4
Rest 4 trouser can be worn with any of the 12 shirts, combination possible=4*12
Total number of combinations=74
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11099
Location: United States (CA)
Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

### Show Tags

03 Apr 2019, 16:59
2
Abhijeet007 wrote:
Sam has 8 trousers and 12 shirts. 2 particular trousers can never be worn with any one of 3 particular shirts, and 2 other particular trousers must be worn with any one of 4 other particular shirts. In how many ways can Sam match up a trouser with a shirt?

(A) 94
(B) 88
(C) 66
(D) 82
(E) 74

Source:- EduShastra Class Sheet.

For the 2 particular trousers that can never be worn with any one of 3 particular shirts, each has 9 shirts to pair with, so there are 2 x 9 = 18 pairings.

For the 2 other particular trousers that must be worn with any one of 4 other particular shirts, there are 2 x 4 = 8 pairings.

For the remaining 4 trousers, each has 12 shirts to pair with, so there are 4 x 12 = 48 pairings.

Therefore, the total is 18 + 8 + 48 = 74 pairings.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

214 REVIEWS

5-STARS RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be   [#permalink] 03 Apr 2019, 16:59