Data Sufficiency

At a particular school, 60 male students play sports. How many male students attend the school?

1. At the school, 3/4 of the female students play sports.
2. At the school, 1/4 of the students do not play sports.

The OA is C.

Why it can't be B?

3/4 of total play sports, so if there are m males and f females then 3/4(m+f) play sports i.e. 3/4m + 3/4f.

However, we know 60 males play sports so 3/4m = 60 and m = 80

We don't need statement 1 for that.

Someone help, please! Thanks in advance!

BTGmoderatorLU wrote:At a particular school, 60 male students play sports. How many male students attend the school?

1. At the school, 3/4 of the female students play sports.
2. At the school, 1/4 of the students do not play sports.

The OA is C.

Why it can't be B?

3/4 of total play sports, so if there are m males and f females then 3/4(m+f) play sports i.e. 3/4m + 3/4f.

However, we know 60 males play sports so 3/4m = 60 and m = 80

We don't need statement 1 for that.

Someone help, please! Thanks in advance!

Hi BTGmoderatorLU.

Interesting, but it's not true your approach.

Let's suppose for a moment that there are 80 male and 20 female students.

So, if 1/4 of the students do not play sports, then we are telling that 25 students do not play sports.

Now, we could have the case where all female and 5 male students do not play sports. It implies that 75 male students play sports, and as we can see, 75 is not the same as 3/4m. So, the second statement alone is not sufficient.

If we use both statements together, we will get:

1. At the school, 3/4 of the female students play sports.

This implies that the number of students that play sports is $$\frac{3}{4}\cdot f\ +\ 60$$

2. At the school, 1/4 of the students do not play sports.

This implies that 3/4 of the students play sports. So, we get the following equation: $$\frac{3}{4}\cdot Total=\frac{3}{4}\cdot f\ +\ 60$$ $$\Rightarrow\ \ \frac{3}{4}\cdot\left(f+m\right)=\frac{3}{4}\cdot f\ +\ 60$$ $$\Rightarrow\ \ \frac{3}{4}\cdot f+\frac{3}{4}\cdot m=\frac{3}{4}\cdot f\ +\ 60$$ $$\Rightarrow\ \ \frac{3}{4}\cdot m=60$$ $$\Rightarrow\ m=80.$$

So, there are 80 male students that attend the school. Sufficient.

The answer is the option C.