carcass wrote:
Last year \(\frac{3}{5}\) of the members of a certain club were males. This year the members of the club include all the members from last year plus some new members. Is the fraction of the members of the club who are males greater this year than last year?
(1) More than half of the new members are male.
(2) The number of members of the club this year is \(\frac{6}{5}\) the number of members last year.
Given:
1. Last year 3/5 of the members of a certain club were males.
Let m be male members and f be female members; m=3k; f=2k; m+f = 5k
2. This year the members of the club include all the members from last year plus some new members.
Asked: Is the fraction of the members of the club who are males greater this year than last
(1) More than half of the new members are male.
Since 1/2 < 3/5; NOT SUFFICIENT
(2) The number of members of the club this year is 6/5 the number of members last year.
The number of members of the club this year = 6/5 * 5k = 6k
Since number of male members out of new k members is unknown
NOT SUFFICIENT
(1) + (2)
(2) The number of members of the club this year is 6/5 the number of members last year.
The number of members of the club this year = 6/5 * 5k = 6k
(1) More than half of the new members are male.
New male members > 3k + k/2 = 3.5k
The fraction of the members of the club who are males this year > 3.5k/6k = 7/12 = 58.33%
Since The fraction of the members of the club who are males last year = 3/5 = 60%
NOT SUFFICIENT
IMO E
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com