Data Sufficiency

Hello Everyone,

Please help me in answering the following Data Sufficiency question from GMATPrep:

What fraction of this year's graduating students at a certain college are males?

1. Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from another college.
2. Of this year's graduating students, 25 percent transferred from another college.

Please let me know what do you think is the correct answer...

What fraction of this year's graduating students at a certain college are males?

1) Of this year's graduating students, 33% of the males and the 20% of the females transferred from another college.

2) Of this year's graduating students, 25% transferred from another college.

Neither statement alone is sufficient to determine males/total.
When the statements are combined, the result is a WEIGHTED AVERAGE/MIXTURE problem:
Of all the men, the percentage who transferred from another college = 33%.
Of all the women, the percentage who transferred from another college = 20%.
Of all the students -- the MIXTURE of men and women -- the percentage who transferred from another college = 25%.

We can use ALLIGATION to determine males/total.

Step 1: Plot the 3 percentages on a number line, with the percentage for the men and women (33% and 20%) on the ends and the percentage for all the students (25%) in the middle.
M 33---------25----------20 W

Step 2: Calculate the distances between the percentages.
M 33----8----25----5-----20 W

Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 5:8.

Since 5+8=13, of every 13 students, 5 are men and 8 are women.
Thus, males/total = 5/13.
SUFFICIENT.

The correct answer is C.

Please note the following:
Almost NO MATH is needed here if we understand how WEIGHTED AVERAGES work.
Statement 1 indicates the percentages for the two INGREDIENTS (the men and the women).
Statement 2 indicates the percentage for the MIXTURE (the men and women combined).
If we know the percentages for the two ingredients and the percentage for 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 the two statements combined are SUFFICIENT to determine males/total.

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

Thanks so much Mitch for providing the solution. The answer is correct.
I am yet to work on the Alligation topic...hope I am able to use it in solving questions soon!!

Thank you Brent for providing the solution. Answer to the DS question is correct i.e. C but I am a little confused now.
The answer given by you for fraction of males is 1/3 whereas the one by Mitch is 5/13. Had it been a problem solving question...what should have been my answer :roll:

Thanks and Regards,
DevB

DevB wrote:Thank you Brent for providing the solution. Answer to the DS question is correct i.e. C but I am a little confused now.
The answer given by you for fraction of males is 1/3 whereas the one by Mitch is 5/13. Had it been a problem solving question...what should have been my answer :roll:

Thanks and Regards,
DevB

The problem that you posted indicates the following:
33 percent of the males transferred from another college.
I used this value in my solution above.
Brent's version of the problem includes a different statistic:
35 percent of the males transferred from another college.
Hence, his solution yields a different result.

Thank u Mitch!

The alternate Solution

Hi All ,

One thing why we conclude below?

So, we can conclude that 0.33M + 0.2F = 0.25(M+F)

Please advise.

Thanks ,

Shreyans