Answer is (C)

Total Student = 105

Condition 1: F:S = 1:2 (alone not sufficient, as does not tell about Juniors)
Condition 2: F:J = 1:4 (alone not sufficient, as does not tell about Sophomore)

When you take both the conditions together, you have a relationship between F and S and J

F:S:J = 1:2:4

and you know the total number of students, so you can calculate the values F, S, & J (In real GMAT, you need not to calculate as it is DS question).

Hence (C) is the answer.

PS: I have seen most of the DS questions of GMAT can be solved without even touching the pen, the above one is just an example of such category.

Have Fun!