Every member of a certain club…
We are given that every member of a club contributes evenly to a $60 gift certificate. We must determine the number of members in the club.
Statement One Alone:
Each member’s contribution is to be $4.
If we let n = the number of members in the club, we can create the following equation:
4n = 60
n = 15
There are 15 members in the club. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
If 5 club members fail to contribute, the share of each contributing member will increase by $2.
If we let n = the number of members in the club, we can say that the amount per person when everyone pays is 60/n and the amount per person when 5 members don’t pay is 60/(n-5). Using 60/n and 60/(n-5), along with the information in statement two, we can create the following equation.
60/(n-5) = (60/n) + 2
We see that we have enough information to determine n, and thus statement two is sufficient; however, we show the completed work below.
When we multiply the entire equation, 60/(n-5) = (60/n) + 2, by n(n-5) we obtain:
60n = 60(n – 5) + 2n(n – 5)
60n = 60n – 300 + 2n^2 – 10n
2n^2 – 10n – 300 = 0
We can divide the entire equation by 2.
n^2 – 5n –150 = 0
(n – 15)(n + 10) = 0
n = 15 or n = -10
Since we cannot have negative value for the number of people in the club, we are left with n = 15. Statement two alone is sufficient to answer the question.