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What fraction of this year's graduating students at a [#permalink]

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22 Jul 2010, 05:32

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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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

Question: \(\frac{m}{m+f}=?\)

Obviously taken separately each statement is not sufficient.

(1)+(2) # of transferred students from (1) equals to \(033m+0.2f\) and from (2) it equals to \(0.25(m+f)\) --> \(0.33m+0.2f=0.25m+0.25f\) --> \(\frac{m}{f}=\frac{5}{8}\) --> \(\frac{m}{m+f}=\frac{5}{13}\). Sufficient.

Without doing any maths calculation, the reasoning is as follows:

We need to know the percentage of male students, in other words the relationship between number of male student (M) and female student (F). This is known when you dispose an (linear) equation of M and F, something like 5M+7F=2M+15F. Statement 1 cannot make this kind of equation, statement 2 neither. Nevertheless, sharing same intermediate variable of students transferred from another college, both of statements can make an equation.

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

Question: \(\frac{m}{m+f}=?\)

Obviously taken separately each statement is not sufficient.

(1)+(2) # of transferred students from (1) equals to \(033m+0.2f\) and from (2) it equals to \(0.25(m+f)\) --> \(0.33m+0.2f=0.25m+0.25f\) --> \(\frac{m}{f}=\frac{5}{8}\) --> \(\frac{m}{m+f}=\frac{5}{13}\). Sufficient.

Answer: C.

Hi Bunuel,

I understand what you did here, but I still don't understand how this is the number of total males over total students. To me, it looks like this is the total of males who transferred in to the total number of students who transferred in. What am I missing?

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

Question: \(\frac{m}{m+f}=?\)

Obviously taken separately each statement is not sufficient.

(1)+(2) # of transferred students from (1) equals to \(033m+0.2f\) and from (2) it equals to \(0.25(m+f)\) --> \(0.33m+0.2f=0.25m+0.25f\) --> \(\frac{m}{f}=\frac{5}{8}\) --> \(\frac{m}{m+f}=\frac{5}{13}\). Sufficient.

Answer: C.

Hi Bunuel,

I understand what you did here, but I still don't understand how this is the number of total males over total students. To me, it looks like this is the total of males who transferred in to the total number of students who transferred in. What am I missing?

\(m\) and \(f\) are the number of graduating males and females respectively, so \(\frac{m}{m+f}=\frac{5}{13}\) is the fraction of graduating males (the fraction of males transferred would be \(\frac{033m}{033m+0.25f}\)).

Sorry Bunuel for a late reply. I meant the question states only the transferring students from other colleges, what about the existing ones? Thx

What about them?

m is the total number of males (including those who transferred and existing ones) and f is the total number of females (including those who transferred and existing ones).

Given that \(0.33m+0.2f=0.25(m+f)\), from which we can find the value of \(\frac{m}{m+f}\).
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Re: What fraction of this year's graduating students at a [#permalink]

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21 Jan 2016, 01:20

sunland wrote:

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

This is a weighted average problem (1) We are not given the ratio between M and F. Not sufficient (2) Clearly not sufficient. (1) + (2) M(33)....8....25......5.....(20)F --> M/F=5/8 and M/m+f=5/13

Answer C
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Re: What fraction of this year's graduating students at a [#permalink]

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18 Oct 2016, 14:20

my method: expressing male/graduation class = m/n in terms of males who transferred, mt. ft is female who transferred. 1. Nominator: m=3mt (from mt=1/3m) 2. Denominator: i. n=4*nt (nt=people who transferred=1/4n) ii. nt=1/4=xmt+(1-x)ft (trying to express n in function of nt in function of mt, and to do so weighted average of mt and ft must equal 1/4) -> find proportion of mt in nt iii. nt=1/xmt iv.n=4*1/xnt

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered 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

Answer: C
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Re: What fraction of this year's graduating students at a [#permalink]

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30 Nov 2016, 19:50

Bunuel wrote:

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

Question: \(\frac{m}{m+f}=?\)

Obviously taken separately each statement is not sufficient.

(1)+(2) # of transferred students from (1) equals to \(033m+0.2f\) and from (2) it equals to \(0.25(m+f)\) --> \(0.33m+0.2f=0.25m+0.25f\) --> \(\frac{m}{f}=\frac{5}{8}\) --> \(\frac{m}{m+f}=\frac{5}{13}\). Sufficient.

Answer: C.

Just wondering since we are supposed to find the fraction and not the exact value. The first statement says that 33% of the students are male. So if we assume the total number of student is 100 then total males if 33. Even if the number increases by any factor the empirical value will always remain 33/100. Giving Answer as A

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 transfered from another college. (2) Of this year's graduating students, 25 percent transfered from another college.

Question: \(\frac{m}{m+f}=?\)

Obviously taken separately each statement is not sufficient.

(1)+(2) # of transferred students from (1) equals to \(033m+0.2f\) and from (2) it equals to \(0.25(m+f)\) --> \(0.33m+0.2f=0.25m+0.25f\) --> \(\frac{m}{f}=\frac{5}{8}\) --> \(\frac{m}{m+f}=\frac{5}{13}\). Sufficient.

Answer: C.

Just wondering since we are supposed to find the fraction and not the exact value. The first statement says that 33% of the students are male. So if we assume the total number of student is 100 then total males if 33. Even if the number increases by any factor the empirical value will always remain 33/100. Giving Answer as A

Can you please elaborate on this.

The red part is not correct. (1) says "Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from another college".

Also, it's not clear what you mean by part in blue.
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Re: What fraction of this year's graduating students at a [#permalink]

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31 Jan 2017, 16:56

let's say M is the # of males in the graduating class (total), and F is the # of females. then statement (1) says 0.33M + 0.20F were transfers; statement (2) says 0.25(M + F) were transfers (i.e., 25% of everybody).

since both of these are the # of transfers, set them equal: 0.33M + 0.20F = 0.25M + 0.25F 0.08M = 0.05F this gives you the ratio of males to females. Sufficient. Hence C.
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