How many members are there? HELP

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gmatpup: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Sat Oct 15, 2011 6:38 pm; Thanked: 1 times; Followed by:1 members

How many members are there? HELP

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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Source: Beat The GMAT — Problem Solving | Fri Dec 23, 2011 6:34 pm

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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.
1-800-566-4043 (USA)

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