Needgmat wrote:All of the 540 people who attended an education convention were either teachers or administrators. There were twice as many females as males at the convention and 3 times as many teachers as administrators. If 1/3 of the administrators were males, how many of the females were teachers?
A) 90
B) 135
C) 180
D) 270
E) 405
Test the SMALLEST POSSIBLE CASE in the following double-matrix:
1/3 of the administrators were males.
Let the total number of administrators = 3, implying 1 male administrator and 2 female administrators.
The following matrix is yielded:
There were 3 times as many teachers as administrators.
The following matrix is yielded:
There were twice as many females as males.
The following matrix is yielded:
Completing the matrix, we get:
How many of the females were teachers?
In the completed matrix, 6 of the 12 attendees are female teachers.
Since 6/12 = 1/2, half of the actual total number of attendees -- 540 -- must be female teachers:
(1/2)(540) = 270.
The correct answer is
D.
Last edited by
GMATGuruNY on Wed Aug 31, 2016 5:29 am, edited 1 time in total.
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