GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 09:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 May 2009
Posts: 143
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]

### Show Tags

28 Mar 2013, 12:48
4
22
00:00

Difficulty:

35% (medium)

Question Stats:

78% (03:06) correct 22% (03:02) wrong based on 528 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59590
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

28 Mar 2013, 13:15
9
2
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.

Attachment:

Teachers.png [ 5.89 KiB | Viewed 11044 times ]

_________________
Manager
Joined: 24 Jan 2013
Posts: 64
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

28 Mar 2013, 17:57
9
1
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 10743 times ]

##### General Discussion
Director
Joined: 17 Dec 2012
Posts: 623
Location: India
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

28 Mar 2013, 23:34
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
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Manager
Joined: 24 Jan 2013
Posts: 64
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

29 Mar 2013, 03:33
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: 623
Location: India
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

29 Mar 2013, 03:36
1
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.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
SVP
Joined: 06 Sep 2013
Posts: 1545
Concentration: Finance
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

27 Feb 2014, 14:04
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
Retired Moderator
Joined: 20 Dec 2013
Posts: 166
Location: United States (NY)
GMAT 1: 640 Q44 V34
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q49 V40
GPA: 3.16
WE: Consulting (Venture Capital)
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

27 Feb 2014, 17:49
1
1
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)
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

08 Jul 2014, 22:59
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 9289 times ]

Manager
Status: tough ... ? Naaahhh !!!!
Joined: 08 Sep 2015
Posts: 62
Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

09 Dec 2015, 09:53
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.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15669
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

29 Jan 2018, 15:34
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

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 13727
Re: All of the 540 people who attended an education convention were either  [#permalink]

### Show Tags

14 Feb 2019, 05:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: All of the 540 people who attended an education convention were either   [#permalink] 14 Feb 2019, 05:31
Display posts from previous: Sort by