Of 1400 college teachers surveyed

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Sat Feb 09, 2013 1:30 pm
Thanked: 4 times

Of 1400 college teachers surveyed

by Zarrolou » Sun Mar 03, 2013 12:34 am
Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?

A) In survey 36% of men and 50% of women said they considered research essential

B) 288 men said they considered research essential

How can I solve this type of questions?
Thanks

OA A

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sun Mar 03, 2013 5:02 am
Zarrolou wrote:Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?

A) In survey 36% of men and 50% of women said they considered research essential
B) 288 men said they considered research essential
Let us assume number of women teacher surveyed was W.
Hence, number of men teacher surveyed was (1400 - W)

Statement 1: 36% of men + 50% of women = 42% of 1400
Hence, 36*(1400 - W) + 50*W = 42*1400
We can solve W from the above equation.

Sufficient

Statement 2:As we don't know the number of men or percentage of men in the total number of people surveyed, we cannot determine W.

Not sufficient

The correct answer is A.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Mar 03, 2013 7:45 am
Zarrolou wrote:Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?

A) In survey 36% of men and 50% of women said they considered research essential

B) 288 men said they considered research essential

How can I solve this type of questions?
Thanks

OA A
This is a WEIGHTED AVERAGE/MIXTURE problem.

Statement 1:
Of all the men, the percentage who considered research essential = 36%.
Of all the women, the percentage who considered research essential = 50%.
Of all the teachers -- the MIXTURE -- the percentage who considered research essential = 42.

To determine the ratio of men to women, use ALLIGATION -- a very efficient way to handle mixture problems.

Step 1: Plot the 3 percentages on a number line, with the two percentages for the two subgroups (36% and 50%) on the ends and the percentage for all the teachers (42%) in the middle.
M(36%)---------42---------W(50%)

Step 2: Calculate the distances between the percentages.
M36%)----6----42----8----W(50%)

Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 8:6 = 4:3.

Since there are 1400 teachers, and M:W = 4:3 = 400:300 = 800:600, W=600.
SUFFICIENT.

Statement 2:
No way to determine the number of women.
INSUFFICIENT.

The correct answer is A.

Please note the following:
Almost NO MATH is needed here if we understand how WEIGHTED AVERAGES work.
Statement 1 indicates the percentage attributed to each INGREDIENT (the men and the women).
The question stem indicates the percentage attributed to the MIXTURE (all of the teachers).
If we know the percentage attributed to each ingredient and the percentage attributed to the mixture, we can ALWAYS determine the RATIO of the two ingredients (in this case, M:W).

Thus -- without doing any math -- we can see that statement 1 is SUFFICIENT to determine how many of the 1400 teachers are women.

Other alligation problems:
https://www.beatthegmat.com/mixture-prob ... tml#593241
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

by gmattesttaker2 » Wed Apr 23, 2014 6:25 pm
GMATGuruNY wrote:
Zarrolou wrote:Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?

A) In survey 36% of men and 50% of women said they considered research essential

B) 288 men said they considered research essential

How can I solve this type of questions?
Thanks

OA A
This is a WEIGHTED AVERAGE/MIXTURE problem.

Statement 1:
Of all the men, the percentage who considered research essential = 36%.
Of all the women, the percentage who considered research essential = 50%.
Of all the teachers -- the MIXTURE -- the percentage who considered research essential = 42.

To determine the ratio of men to women, use ALLIGATION -- a very efficient way to handle mixture problems.

Step 1: Plot the 3 percentages on a number line, with the two percentages for the two subgroups (36% and 50%) on the ends and the percentage for all the teachers (42%) in the middle.
M(36%)---------42---------W(50%)

Step 2: Calculate the distances between the percentages.
M36%)----6----42----8----W(50%)

Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 8:6 = 4:3.

Since there are 1400 teachers, and M:W = 4:3 = 400:300 = 800:600, W=600.
SUFFICIENT.

Statement 2:
No way to determine the number of women.
INSUFFICIENT.

The correct answer is A.

Please note the following:
Almost NO MATH is needed here if we understand how WEIGHTED AVERAGES work.
Statement 1 indicates the percentage attributed to each INGREDIENT (the men and the women).
The question stem indicates the percentage attributed to the MIXTURE (all of the teachers).
If we know the percentage attributed to each ingredient and the percentage attributed to the mixture, we can ALWAYS determine the RATIO of the two ingredients (in this case, M:W).

Thus -- without doing any math -- we can see that statement 1 is SUFFICIENT to determine how many of the 1400 teachers are women.

Other alligation problems:
https://www.beatthegmat.com/mixture-prob ... tml#593241

Hello Mitch,

Thanks for the explanation. I just had a question here:
Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 8:6 = 4:3.
I was just thinking that does this mean that the number of women who consider research essential (out of 42) = 3x = 18 and that the number of men who consider research essential (out of 42) = 4x = 24

=> 18/42 = ?/1400
=> Women who consider research essential = 600

Is this correct?

Also, since we get from here that the men who consider research essential = 800, I was just wondering what the 288 that is mentioned in Statement 2 means?

Thanks for your help.

Best Regards,
Sri