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How many members are there? HELP

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by gmatpup » Fri Dec 23, 2011 6:34 pm
Two members of a club are to be selected for a meeting. If there are 190 different possible selections of the 2 members, how many members are there?

A. 20
B. 27
C. 40
D. 57
E. 95


How do I solve this? Thank you !!

Answer is A
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by Anurag@Gurome » Fri Dec 23, 2011 7:02 pm
gmatpup wrote:Two members of a club are to be selected for a meeting. If there are 190 different possible selections of the 2 members, how many members are there?

A. 20
B. 27
C. 40
D. 57
E. 95


How do I solve this? Thank you !!

Answer is A
Let there are M members to choose from.
Now MC2 = 190
M!/[2! * (M - 2)!] = 190
M * (M - 1) * (M - 2)!/[2! * (M - 2)!] = 190
M(M - 1) = 190 * 2
M(M - 1) = 380, which implies we have to find two consecutive numbers whose product is 380. Look at the given answer choices.
(A) If M = 20, then M - 1 = 19, and their product = 380

The correct answer is A.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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