Video Explanation

Text Explanation

Start by assigning variables to the number of freshmen and number of seniors:

We know that S + F = 42. Now let's look at statement 1, which says that the group has more than four times as many seniors as freshmen. Translated into math, that's 4F < S. Let's try some possible values for F and S:

The number of freshmen can't be 9 because four times that is 36. That would make the total number of students 9+36 = 45, which is more than 42. Statement 1 helps us narrow down the list of possible numbers of seniors and freshmen, but does not help us find one value. It's insufficient.

Statement 2 says that the group has more than 7 freshmen, That means F>7. There are LOTS of possible values for this, anything from 8 freshmen all the way up to 30 freshmen:

Statement 2 is insufficient. Interestingly, if we combine both statements, they are sufficient. Statement 1 goes up to 8 freshmen and 34 seniors, and statement 2 starts at 8 freshmen and 34 seniors. This is the one and only set of values where the two lists overlap. That means that together the statements are sufficient, and the answer is (C):