All of the 540 people who attended an education convention were either

Question

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.

(A) 90
(B) 135
(C) 180
(D) 270
(E) 405

Bunuel · Accepted Answer

Total = 540 people.

Twice as many females as males --> (Female) = 360 and (Males) = 180.

3 times as many teachers as administrators --> (Teachers) = 405 and (Administrators) = 135.

1/3 of the administrators were males --> (Male Administrators) = 135*1/3 = 45.

Make a matrix:

So, (Female Teachers) = 270.

Answer: D.

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Attachment:

Teachers.png

johnwesley · Answer

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

SVaidyaraman · Answer

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

johnwesley · Answer

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. :wink:

SVaidyaraman · Answer

Yes johnwesley, the grid method is faster. But if it is possible to adopt a more or less uniform approach to problems, you may gain on the average.

jlgdr · Answer

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

m3equals333 · Answer

one way to solve in 30 secs is if you can make the below connection very quickly:

Females comprise 2/3 of conference
Females comprise 2/3 of admin, so they must also comprise 2/3 of teachers (so female teachers comprise 2/3*3/4 = 1/2 of conference)

PareshGmat · Answer

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

asethi · Answer

I think the fastest way would be

A+T=540,
A=3T so T=135 and A=405

Male=A/3, so Male=135 and the remaining 270 will be females.

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

ArnauG · Answer

Let's solve the problem step by step.

Given:

Total attendees at the convention = 540
All attendees are either teachers or administrators
Number of females = 2 * number of males
Number of teachers = 3 * number of administrators
1/3 of administrators are males
Let's calculate the number of males and females at the convention:

Number of females = 2 * number of males
Number of males + Number of females = 540

Substituting the first equation into the second equation:
Number of males + 2 * number of males = 540
3 * number of males = 540
Number of males = 540 / 3
Number of males = 180

Number of females = 2 * number of males
Number of females = 2 * 180
Number of females = 360

Now, let's calculate the number of administrators and teachers:

Number of teachers = 3 * number of administrators

Number of administrators + Number of teachers = 540

Substituting the first equation into the second equation:
Number of administrators + 3 * number of administrators = 540
4 * number of administrators = 540
Number of administrators = 540 / 4
Number of administrators = 135

Since we know that there are 3 times as many teachers as administrators:
Number of teachers = 3 * 135
Number of teachers = 405

Finally, we need to calculate the number of females who are teachers:
Number of females who are teachers = 2/3 * Number of teachers
Number of females who are teachers = 2/3 * 405
Number of females who are teachers = 270

Therefore, the correct answer is (D) 270.

Ved111 · Answer

Good way to solve using matrix, linear equation view took some more time

All of the 540 people who attended an education convention were either

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