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#593241Private 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
Thank u Mitch!
