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by Night reader » Fri Dec 03, 2010 10:47 pm
Two members of a certain club are selected to speak at the next club meeting.
If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
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by shovan85 » Fri Dec 03, 2010 10:50 pm
Night reader wrote:Two members of a certain club are selected to speak at the next club meeting.
If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
IMO E

C(n,2) = 36

=> n!/[ ( n - 2 ) ! * 2 ! ] = 36

=> n * (n-1) = 72

=> n = 9 (as 8*9 = 72)
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by Rahul@gurome » Fri Dec 03, 2010 10:54 pm
Night reader wrote:Two members of a certain club are selected to speak at the next club meeting.
If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
Say, there are n members in the club.

Number of ways to select 2 member out of n member = nC2
= n!/[(n - 2)!*(2!)]
= n(n - 1)/2

According to question, n(n - 1)/2 = 36
=> n(n - 1) = 72

Now we can solve this quadratic expression which is a lengthy and complicated method or we can look for two consecutive integers whose product is 72. In this case they are 8 and 9. Thus, n = 9.

The correct answer is E.
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by Night reader » Fri Dec 03, 2010 11:03 pm
Rahul@gurome wrote:
Night reader wrote: Now we can solve this quadratic expression which is a lengthy and complicated method or we can look for two consecutive integers whose product is 72. In this case they are 8 and 9. Thus, n = 9.

The correct answer is E.
or we can use foil for n^2-n-72=0

n^2 + (a+b)*n + (ab)*n =0
n^2 + (8+[-9])*n + (8*[-9])*n =0 => (n+8)(n-9)

with k=2 simplify as shovan did n*(n-1)/2 = 36

whichever way is attractive and first on mind :)
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by GMATGuruNY » Sat Dec 04, 2010 4:05 am
Night reader wrote:Two members of a certain club are selected to speak at the next club meeting.
If there are 36 different possible selections of the 2 club members, how many members does the club have?

A. 5
B. 6
C. 7
D. 8
E. 9
We can plug in the answer choices, which represent the number of members.

Answer choice C:
7C2 = 21. Too small. Eliminate A, B and C.

Answer choice D:
8C2 = 28. Too small. Eliminate D.

The correct answer is E.

For the skeptical among us, answer choice E:
9C2 = 36.
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