Anaira Mitch wrote:Last year 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 6/5 the number of members last year.
Let the total number of members last year = 50, implying that the number of male members last year = (3/5)(50) = 30.
Question stem, rephrased:
Is (new total males)/(new total members) > 3/5?
Statement 2:
New total members = (6/5)(50) = 60, implying that the number of new members = 10.
No information about the number of new males.
INSUFFICIENT.
Statement 1:
Case 1: new males = 6 and new females = 4, for a total of 10 new members
In this case:
(new total males)/(new total members) = (30+6)/(50+10) = 36/60 = 3/5.
Since the fraction of males remains 3/5, the answer to the question stem is NO.
Case 2: new males = 10 and new females = 0, for a total of 10 new members
In this case:
(new total males)/(new total members) = (30+10)/(50+10) = 40/60 = 2/3.
Since the fraction of males > 3/5, the answer to the question stem is YES.
Cases 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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