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What fraction of this year's graduating students

This topic has 2 expert replies and 1 member reply
guerrero Master | Next Rank: 500 Posts
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What fraction of this year's graduating students

Wed Sep 11, 2013 9:13 am
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.

OA
C

Java_85 Master | Next Rank: 500 Posts
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Wed Sep 11, 2013 9:29 am
It's a tricky question, first I thought E is the answer, but after writing the equations, find out C is the right answer.
Here is why:

lets assume :
x=total number of students
xm= number of male student,
xf=number of female students, what the question is asking for is xm/x

Lets write the 2 equations we have:

Equation 1: xm+xf=x
Equation 2 : using (1)(2) --> 33% xm + 20% xf =25% x

2 equations and 3 unknowns ==> U can obtain the xm/x ratio solving them.

Hope this helps.

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GMATGuruNY GMAT Instructor
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Wed Sep 11, 2013 2:19 pm
Quote:
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:
http://www.beatthegmat.com/mixture-problem-rabbit-proteins-t190121.html#593241

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Scott@TargetTestPrep GMAT Instructor
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Tue Dec 05, 2017 5:48 pm
guerrero wrote:
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.
We need to determine what fraction of this year's graduating students at a certain college are males. Since we do not know the number of male and female graduating students in the college, we can let m = the number of male graduating students in the college and f = the number of female graduating students in the college. We need to determine the value of m/(m + f).

Statement One Alone:
Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from another college.

Using the information from statement one, we know that 0.33m = the number of male graduating students who transferred from another college and 0.20f = the number of female graduating students who transferred from another college. However, we cannot determine the value of m/(m + f). Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:
Of this year's graduating students, 25 percent transferred from another college.

Using the information from statement two we know that 0.25(m + f) = the number of graduating students who transferred from another college. However, we still cannot determine m/(m + f). Statement two alone is not sufficient. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two, we know that 0.33m + 0.20f must equal 0.25(m + f). That is,

0.33m + 0.20f = 0.25(m + f)

0.33m + 0.20f = 0.25m + 0.25f

0.08m = 0.05f

8m = 5f

f = 8m/5

Since f = 8m/5, we can substitute 8m/5 in the expression m/(m + f) and we have:

m/(m + 8m/5)

1/(1 + 8/5)

1/(13/5) = 5/13

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