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

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by AAPL » Wed May 27, 2020 4:02 am

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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
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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
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