Let us assume we have 100 students

Out of 100 20% took Writing Class i.e. 20

A. Out of 20 50% also took Maths i.e.: Total 10 students
But we do not know about students who did not take writing classes.
B. 40 % is Math students also took writing class
It is also insufficient

For C we combine both conditions:
Now, we know 40% of x = 10
That means x = 25

So, from C we get the solution

let total = 100
2x2 matrix
---WC--NWC---total
Mat--10-- --- --- .40x
Nm--10--- --- ---.6x
total--20 ---80---100
#1
50 percent of the students who take a writing class also take a math class.
Maths +WC= 10 . but NMC + Maths not know ; insufficient
#2
40 percent of the students who take a math class also take a writing class.
---WC--NWC---total
Mat--a-- --- --- .40x
Nm--20-a--- --- ---.6x
total--20 ---80---100
.4x = a
a not know insufficient

from 1 &2
10=.4x
x= 25
IMO C

If 20 percent of the students at a certain college take a writing class, what percent of the students at the college take a math class?

(1) 50 percent of the students who take a writing class also take a math class.

(2) 40 percent of the students who take a math class also take a writing class.

Q: % taking Math class -> (Math class & Writing Class) + (Math class & Not Writing Class)

i) we know 20 take writing class -> 50% (20) take math class as well -> help us know how many take Math class and Writing class together -> i.e. (Math Class + Writing Class) = 10 -> Insufficient to know Math class percentage (since we don't know what math class and Not Writing Class % is)

ii) we don't know what Math class percentage is (say x). Then \(\frac{2}{5*x}\) = (Math Class + Writing Class) -> Insufficient since we don't know how many take Math Class + writing class amongst [Math class & Writing Class + Math class & Not writing Class]

Combining i) and ii) we know (Math Class + Writing Class) = 10 = \(\frac{2}{5*x}\) -> Sufficient to know x

Answer - C
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