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

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Manager
Joined: 28 May 2009
Posts: 154
Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
All of the 540 people who attended an education convention were either [#permalink]

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28 Mar 2013, 11:48
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Difficulty:

35% (medium)

Question Stats:

78% (02:23) correct 22% (02:12) wrong based on 464 sessions

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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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43828
Re: All of the 540 people who attended an education convention were either [#permalink]

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28 Mar 2013, 12:15
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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.

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.

[Reveal] Spoiler:
Attachment:

Teachers.png [ 5.89 KiB | Viewed 7209 times ]

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Manager
Joined: 24 Jan 2013
Posts: 75
Re: All of the 540 people who attended an education convention were either [#permalink]

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28 Mar 2013, 16:57
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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

Attachments

Imagen1.jpg [ 41.78 KiB | Viewed 7040 times ]

Director
Joined: 17 Dec 2012
Posts: 627
Location: India
Re: All of the 540 people who attended an education convention were either [#permalink]

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28 Mar 2013, 22:34
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

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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Srinivasan Vaidyaraman
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http://www.sravnatestprep.com

Standardized Approaches

Manager
Joined: 24 Jan 2013
Posts: 75
Re: All of the 540 people who attended an education convention were either [#permalink]

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29 Mar 2013, 02:33
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.

Director
Joined: 17 Dec 2012
Posts: 627
Location: India
Re: All of the 540 people who attended an education convention were either [#permalink]

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29 Mar 2013, 02:36
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Expert's post
johnwesley wrote:
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.

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.
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Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Standardized Approaches

Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance
Re: All of the 540 people who attended an education convention were either [#permalink]

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27 Feb 2014, 13:04
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
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Joined: 20 Dec 2013
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Re: All of the 540 people who attended an education convention were either [#permalink]

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27 Feb 2014, 16:49
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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)
_________________
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Re: All of the 540 people who attended an education convention were either [#permalink]

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08 Jul 2014, 21:59
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

Attachments

tea.jpg [ 17.76 KiB | Viewed 5606 times ]

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Manager
Status: tough ... ? Naaahhh !!!!
Joined: 07 Sep 2015
Posts: 65
Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)
Re: All of the 540 people who attended an education convention were either [#permalink]

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09 Dec 2015, 08:53
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.
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Re: All of the 540 people who attended an education convention were either [#permalink]

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29 Jan 2018, 14:34
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...

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

135 - 45 = 90 female administrators

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

360 total females
360 - 90 = 270 female teachers

[Reveal] Spoiler:
D

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Re: All of the 540 people who attended an education convention were either   [#permalink] 29 Jan 2018, 14:34
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