Data Sufficiency

Q: What fraction of this year's graduation students at a certain college are males?
(1) Of this year's graduation students, 35% of male and 20% of female transferred from another college.
(2) Of this year's graduation students, 25% transferred from another college.

A: According to me should have been E, [spoiler]reason being that we don't know the population of Male/Female students who are't a transfer[/spoiler]?

MI3 wrote:Q: What fraction of this year's graduation students at a certain college are males?
(1) Of this year's graduation students, 35% of male and 20% of female transferred from another college.
(2) Of this year's graduation students, 25% transferred from another college.

A: According to me should have been E, [spoiler]reason being that we don't know the population of Male/Female students who are't a transfer[/spoiler]?

No math is needed. This is a classic mixture problem.
The MEN and WOMEN are being combined into a MIXTURE of men and women.

DS questions above mixtures typically involve 3 key facts:

FACT 1: The percentage in each ingredient.
FACT 2: The ratio of the ingredients in the mixture.
FACT 3: The resulting percentage in the mixture.

Given FACT 1 (the percentage in each ingredient() and FACT 2 (the ratio of the ingredients), we can determine FACT 3 (the resulting percentage in the mixture).
Given FACT 1 (the percentage in each ingredient) and FACT 3 (the resulting percentage in the mixture), we can determine FACT 2 (the ratio of the ingredients).

Combining the two statements in the DS question above:
MEN = 35% transfer.
WOMEN = 20% transfer:
The resulting MIXTURE of men and women = 25% transfer.

Since we're given FACT 1 (the percentage in each ingredient) and FACT 3 (the resulting percentage in the mixture), we can determine FACT 2 (the ratio of the ingredients -- in other words, the ratio of MEN to WOMEN).

The correct answer is C.

Hello Mitch,

Thank you for coming back to me on this, but I am still not a 100% clear. A couple of my queries are mentioned below, if you may:

1. How do you identify that it is a weighted average/mixture problem?
2. Do we not need to consider other sects of population - i.e. those who aren't a transfer?

I have the same question as M13.
Do we not need to consider those who are not transfer students?

For example, it might be a drastic example but let's assume that the school was all-boys college and the school just takes women as transfer students. If this is so, we could know the ratio of male/female by using the two given conditions, but if we consider the overall graduation ratio, male would be much higher?

Anyone who know, please provide an explanation. Thanks!

MI3 wrote:Hello Mitch,

Thank you for coming back to me on this, but I am still not a 100% clear. A couple of my queries are mentioned below, if you may:

1. How do you identify that it is a weighted average/mixture problem?
2. Do we not need to consider other sects of population - i.e. those who aren't a transfer?

Here is the basic structure of a weighted average question:
Element 1 is X%.
Element 2 is Y%.
A mixture of Element 1 and Element 2 is Z%.

The DS question above is structured exactly this way:
The graduating men are 35% transfer.
The graduating women are 20% transfer.
When the men and women are combined, the resulting graduating class is 25% transfer.

Given the information above, we can determine the ratio of men to women in the graduating class.

One method is alligation. Alligation is used to determine how much weight must be given to each element in the mixture. Simply stated:

The proportion of each element in the mixture is the distance between the other two percentages.

Proportion of men = Class % - Women's % = 25-20 = 5.
Proportion of women = Men's % - Class % = 35-25 = 10.

The results above give us the ratio of men to women:
M:W = 5:10 = 1:2.

Since 1+2=3, the men are 1/3 = 33.34% of the class.

To illustrate:
Men = 100, Women = 200, Class = 300.
35% of the men are transfers = .35*100 = 35.
20% of the women are transfers = .2*200 = 40.
Total transfers = 35+40 = 75.
Total transfers/Total class = 75/300 = 25/100 = 25%.

As I noted in my original post, none of this math is needed in the DS question above. Given the info in the two statements, we have sufficient information to determine the ratio of men to women.

Hi Mitch,

I have a question.

When I first looked at this question, I marked the answer as E because both the choices talk about percent of transferred students and the question asks about percentage of males graduating from a certain college. But you have figured out the percent of transferred students (male) in a certain college.

Isn't it that we have to consider that a certain college might have transferred students from another college who are graduating in college considered in question stem?

Please help.