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by niketdoshi123 » Tue May 08, 2012 12:15 am
Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?

(1) Each member's contribution is to be $4
(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2.
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by mathbyvemuri » Tue May 08, 2012 12:37 am
Statement(1):
sufficient to answer.
number of members = (total contribution)/(individual contribution) = 60/4 = 15

Statement(2):
Let the number be x, which implies each contribution must be 60/x, if all members contribute equally.
"If 5 members fail to contribute, the share of each contributing members will increase by 2" => (x-5)(60/x - 2) = 60
This yields two values for x. But without finding the values, we cannot take any decision.
After solving the equation, we get x = 6 or -10
Negtive value for x can be neglected, as it represents number of members. As there is no ambiguity in the value of x, statement(2) alone is also sufficient

Answer "D"
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by Anurag@Gurome » Tue May 08, 2012 8:28 pm
niketdoshi123 wrote:Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?

(1) Each member's contribution is to be $4
(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2.
Let us assume that the no. of members in the club = N

(1) Each member's contribution is to be $4 implies N = 60/4 = $15; SUFFICIENT.

(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2.
Each member's contribution = 60/N
If 5 club members fail to contribute, then each member's contribution = 60/(N - 5)
It is given that 60/(N - 5) = (60/N) + 2
60/(N - 5) = (60 + 2N)/N
60N = 60N - 300 + 2N² - 10N
N² - 5N - 150 = 0
N² - 15N + 10N - 150 = 0
N(N - 15) + 10(N - 15) = 0
(N - 15)(N + 10) = 0
N = 15; SUFFICIENT.

The correct answer is D.
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