BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

An organization constructs a committee of 3 people from A, B

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Fri Mar 30, 2018 1:01 am
[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members
Location: New Delhi, India
Thanked: 205 times

by GMATinsight » Sat Mar 31, 2018 11:48 pm
Max@Math Revolution wrote:[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45
METHOD 1:

Favourable case = All possible committees of 3 members - Committees of 3 with A and B together in it
7C3 = total ways of selecting 3 members out of 7
5C1 = Since A and B are already selected so we need only one more member out of 5 to make the unwanted teams of 3

i.e. Favourable cases = 7C3 - 5C1 = 35-5 = 30

Answer: option B

METHOD 2:
Case 1: A is selected and B is not = 5C2 = 10
Case 2: B is selected and A is not = 5C2 = 10
Case 3: A and B are both not selected = 5C3 = 10
Total Favourable cases = 10+10+10 = 30

Answer: option B
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Apr 01, 2018 5:37 pm
=>
The total number of possible committees of three 3 people chosen from 7 people is 7C3 = 35.
However, we need to exclude the committees containing both A and B.
The number of committees containing A, B and one other person is equal to the number of ways of choosing 1 person from the C, D, E, F, and G, which is 5C1 = 5.
Therefore, the total number of committees 35 - 5 = 30.

Therefore, the answer is B.
Answer: B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8137
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Wed Apr 04, 2018 4:51 pm
Max@Math Revolution wrote:[GMAT math practice question]

An organization constructs a committee of 3 people from A, B, C, D, E, F and G. A and B are relatives, so they cannot both be committee members at the same time. How many different committees can be formed?

A. 25
B. 30
C. 35
D. 40
E. 45
We can use the formula:

Total number of committees = committees including A and B + committees not including both A and B

Note that since we are choosing 3 people from 7, the total number of committees is:

7C3 = 7!/(4!*3!) = (7*6*5)/(3*2) = 35.

The number of committees including A and B can be found by observing that since A and B already occupy 2 of the 3 available positions, there are 5 choices left for the third person; therefore there are 5 committees including both A and B.

Thus, the number of committees not including both A and B is 35 - 5 = 30.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1