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
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Maybe this helps to achieve the 30 secs you want:

Just multiply 66% x 75% = 50% (SEE ATTACHED FIGURE)

The solution is 50% of 540 ---> 270

Answer D

SravnaTestPrep, maybe it's much faster doing the grid, isn't it? The grid helps to avoid doing calculations that you don't need and gain seconds.

Hey there,

Yes. Grid works best but I its hard to get it all by 30 seconds unless you're really fast on your calculations.

Cheers
J

Females are twice than that of males & total = 540

So, Males = 180; Females = 360

Prepare a chart as shown in diagram below:

We require to find the value of "x" (Female - Teachers)

There are 3 times as many teachers as administrators

x+y = 3 (180+360-x-y)

4(x+y) = 3 * 540

x+y = 405 ............ (1)

1/3rd of the administrators were males

\(\frac{180-y+360-x}{3} = 180-y\)

x = 2y

\(y = \frac{x}{2}\)

Placing value of y in equation (1)

\(\frac{3x}{2} = 405\)

x = 270

Answer = D

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Hi All,

While this question is 'step-heavy', it's really just about doing the necessary arithmetic/algebra and taking organized notes.

We're told that there are 540 total people and that there were TWICE as many females as males....

M = number of Males
F = number of Females

M + F = 540

F = 2M now we'll substitute this into the first equation....

M + 2M = 540
3M = 540
M = 180

So there are 180 males and 360 females

We're also told that there are 3 times as many teachers as administrators (the math works exactly the same as what we just did above, just with different variables). You would end up with...

135 administrators and 405 teachers

Finally, we're told that 1/3 of the administrators were males...

135 total administrators
(1/3)(135) = 45 male administrators
135 - 45 = 90 female administrators

Using this information, with the original deductions (from above), we have...

360 total females
90 female administrators
360 - 90 = 270 female teachers

Final Answer:

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Rich
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