All of the 540 people who attended an education convention were either teachers or administrators. here 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
OAD
Please explain.
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teachers or administrators
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Hi Needgmat,
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
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
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regor60
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Create a matrix and translate each of the statements into variables:
Male Female Total
Admin A/3 2*A/3 A
Teacher 3*A
Total B 2*B 540
So, A must be 135 and B must be 180.
Therefore, there must be 135 male teachers, since A/3 and the number of male teachers must equal B, 180.
There must also be 270 female teachers by the same logic.
This software stinks...
Male Female Total
Admin A/3 2*A/3 A
Teacher 3*A
Total B 2*B 540
So, A must be 135 and B must be 180.
Therefore, there must be 135 male teachers, since A/3 and the number of male teachers must equal B, 180.
There must also be 270 female teachers by the same logic.
This software stinks...
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Test the SMALLEST POSSIBLE CASE in the following double-matrix:Needgmat 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
1/3 of the administrators were males.
Let the total number of administrators = 3, implying 1 male administrator and 2 female administrators.
The following matrix is yielded:
There were 3 times as many teachers as administrators.
The following matrix is yielded:
There were twice as many females as males.
The following matrix is yielded:
Completing the matrix, we get:
How many of the females were teachers?
In the completed matrix, 6 of the 12 attendees are female teachers.
Since 6/12 = 1/2, half of the actual total number of attendees -- 540 -- must be female teachers:
(1/2)(540) = 270.
The correct answer is D.
Last edited by GMATGuruNY on Wed Aug 31, 2016 5:29 am, edited 1 time in total.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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I thought I'd point out that Mitch's approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- administrator or not an administrator
- female or not male
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
Here, we have a population of students, and the two characteristics are:
- administrator or not an administrator
- female or not male
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Once you're familiar with this technique, you can attempt these additional practice questions:
Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html
Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent
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We could also do it algebraically. Let's start with:
t + a = 540
m + f = 540
2m = f
3a = t
Since 3a = t, we'll sub that into the first equation, to find 3a + a = 540, or a = 135. We can do the same with 2m = f, to find m + 2m = 540, or m = 180.
Now we've got 180 men and 135 administrators. (1/3) of the 135 are men, or 45, so the other 135 guys are teachers.
We know from t + a = 540 that we have 405 teachers. 135 are men, so the other 270 are women, and we're set.
While the numbers here were friendlier than they might be on the test, you can see how quick the algebra can be: I'd have found the answer in about the same time it would have taken me to draw out the matrices!
t + a = 540
m + f = 540
2m = f
3a = t
Since 3a = t, we'll sub that into the first equation, to find 3a + a = 540, or a = 135. We can do the same with 2m = f, to find m + 2m = 540, or m = 180.
Now we've got 180 men and 135 administrators. (1/3) of the 135 are men, or 45, so the other 135 guys are teachers.
We know from t + a = 540 that we have 405 teachers. 135 are men, so the other 270 are women, and we're set.
While the numbers here were friendlier than they might be on the test, you can see how quick the algebra can be: I'd have found the answer in about the same time it would have taken me to draw out the matrices!
