megafan 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

Looking for a 30-sec approach.

Given:

1. No.of people = 540

2. No of males =x, no of females = 2x

3. No of administrators=y, no of teachers = 3y

4. y/3 = male administrators and 2y/3 = female administrators

Question

No of Female teachers?

= Number of Females - Number of Female administrators

= 2x-2y/3

Deductions

1. x + 2x = 540 or x=180.

2. y + 3y = 540 or y=135.

Female teachers = 2x-2y/3 = 360-90=270

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