There are n members in a certain department, including Michael. Two representatives are to be selected...

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

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

There are n members in a certain department, including Michael. Two representatives are to be selected...

by AAPL » Wed May 27, 2020 4:02 am

Timer

00:00

Your Answer

Global Stats

Economist GMAT

There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n?

A. 11
B. 12
C. 15
D. 18
E. 22

OA B

Quote

Source: Beat The GMAT — Problem Solving | Wed May 27, 2020 4:02 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

Re: There are n members in a certain department, including Michael. Two representatives are to be selected...

by Jay@ManhattanReview » Wed May 27, 2020 4:57 am

AAPL wrote: ↑
Wed May 27, 2020 4:02 am
Economist GMAT

There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n?

A. 11
B. 12
C. 15
D. 18
E. 22

OA B

To exclude Michael, we must select 2 reps from (n – 1) members.

# of ways, we can do such = (n – 1)C2 = (n – 1)(n – 2)/1.2 = (n – 1)(n – 2)/2

=> (n – 1)(n – 2)/2 = 55

(n – 1)(n – 2) = 110

Since (n – 1) and (n – 2) are two consecutive integers, we must split 110 such that it a product of two consecutive integers; the larger of the two would be the value of (n – 1).

(n – 1)(n – 2) = 11*10

=> n – 1 = 11

n = 12

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Warangal | Hyderabad | GRE Prep Mumbai | Visakhapatnam GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.