What fraction of this year's graduating students at a certain 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.

Answer: C.
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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.

Therefore correct answer is C.

It should be C.

Let x be the no of males in the college
Let y be the no of females in the college

To find x/x+y


1) From statement 1 we know

.33x and .20y out of x and y transferred from another college. We cant find x+y or x/x+y

Insufficient

2) .25(x+y) transferred from other college. We cant find x/x+y with just this Insufficient

From 1) and 2)
we know
.33x+.20y = .25(x+y)

From this we can find the ratio x/x+y

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 \(\frac{033m}{033m+0.25f}\)).

Hope it's clear.
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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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Oh yeah, sorry may be missed that bit initially. Sorry again for a stupid question. : )

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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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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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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Bunuel how come the answer is different when trying to calculate using fractions?

.33m = m/3
.20f = f/5
.25 (m+f) = (m+f)/4

m/3+f/5=(m+f)/4 -> (5m+3f)/15=(m+f)/4 -> 20m+12f=15m+15f -> 5m=3f or m/f=3/5

In your solution, m/f = 5/8.

What am i forgetting here?

The point is 0.33 does not equal to 1/3.

0.33 = 33/100 while 1/3 = 0.3333....
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chetan2u

Can you please please help me with this question.?

Firstly, I am not convinced on how 1/3 and 33% are not equal (unless we are only considering the recurring 3's after the decimal).

Secondly, I was not able to come up with (m+f) representation of the students so it's unlikely will be able to do it next time as well.

Hi

Whenever you are looking for overall %, average, ratio etc where you have two items(with %, ratio, fraction) that constitute the total, you can find the ratio of the two items in total.
You can use weighted average method or equations.

Weighted average method.
The average / fraction of two groups will be away from the average/fraction when total of these two groups are taken in the ratio of their weight.

Let us try this.
m ..... t .....f
33%..25%..20%
Fraction of m = (t-f)/((m-f)=5/13

Equations
Statement I tells us that 0.33m and 0.20f are from outside
Statement II tells us that overall 25% or o.25 of total students have come from outside.
Now what does this who are total students?- they are m+f, because that is what it would constitute of.
Example we eat 2 apples out of 4 apples that are with us and 1 orange out of 5 oranges we had. So % of each fruit should be equally to overall %....2/4 or 50% of apples and 1/5 or 20% of oranges are eaten. Overall we have eaten 3 out of 9 or 33.33. Thus 0.5(apples)+0.2(oranges)=0.33(total)..0.5*4+0.2*5=0.333*9...2+1=3

Similarly here 0.33m+0.2f=0.25(t)=0.25(m+f)......0.33m-0.25m=0.25f-0.20f....8m=5f....f=8m/5..
Fraction of m = m/(m+f)=m/(m+8m/5)=m/(13m/5)=5/13

Now on 33% and 1/3. If you are on a PS question, it will make a difference unless we are looking for approximation.
Say you are looking for 33% of 300, it is 99, but 1/3 of 300 is 100
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What fraction of this year's graduating students at a certain college are males?

Let Graduating males = Gm and
Graduating females = Gf
Gm / Gm + Gf = ?

(1) Of this year's graduating students, 33 percent of the males and 20 percent of the females transfered from another college.
0.33Gm + 0.20Gf are transferred from another college. We don't know about the relation beween males and females. So,

INSUFFICIENT.

(2) Of this year's graduating students, 25 percent transfered from another college.
0.25(Gm + Gf) are transferred.
Again it is not known what proportion constitutes among males and females in those transferred or even in that certain college.

INSUFFICIENT.

Together 1 and 2.
0.33Gm + 0.20Gf = 0.25(Gm + Gf)
0.07Gm = 0.05Gf

SUFFICIENT.

Answer C.
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Each statement, taken one at a time, is not sufficient.

Taking both statements together:
Let total number of students be t.
Out of these t students, m are male and f are female.
t = m + f

If 25% of total graduating students are transferred then 75% of total graduating students are already present.
Thus, existing students = 0.75 t
transferred students = 0.25 t
If 33% of total graduating male students are transferred then 67% of total graduating male students are already present.
Thus, existing male students = 0.67 m
transferred male students = 0.33 m
If 20% of total graduating female students are transferred then 80% of total graduating female students are already present.
Thus, existing female students = 0.8 f
transferred female students = 0.2 f

Approach 1: If we consider existing students:
Total existing students = total existing male students + total existing female students
0.75 t = 0.67 m + 0.8 f
0.75 (m+f) = 0.67 m + 0.8 f (Substituting t as m+f)
0.75 m + 0.75 f = 0.67 m +0.8 f
0.75 m - 0.67 m = 0.8 f -0.75 f
0.08 m = 0.05 f
m/f = 5/8

Approach 2: Alternatively, if we consider transferred students
Total transferred students = total transferred male students + total transferred female students
0.25t = 0.33m + 0.2f
0.25 (m+f) = 0.33m + 0.2f (Substituting t as m+f)
0.25 m + 0.25 f = 0.33m +0.2f
0.25 f - 0.2 f = 0.33m - 0.25 m
0.05 f = 0.08 m
m/f = 5/8

Ratio of male to female is same in both approaches i.e. m/f = 5/8
Fraction of graduating students who are male = m / t
m/(m+f)= 5/13 (Substituting t as m+f)
Hence, both statements together are sufficient.
C is the correct answer.

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