It may be helpful to put the question in algebraic terms. The tip will be equal to a constant, c, plus an amount that is proportional to the bill: kb, where k is the fraction of the bill, and b is the amount of the bill. So the tip will be c+kb, and since we know the bill for the meal is $24, the tip will be c+24k.

Statement (1) is insufficient. If the bill were $4 greater, that would be a bill of 28, so the equation looks like this:
4.80 = c+28k
There are two variables and only one equation, so we can't solve.

Statement (2) is also insufficient. This gives us another equation with the same variables:
3.80 = c+18k

Taken together, the statements are sufficient. You don't have to do the math: recognize that you have two variables and two distinct linear equations. If you do want to solve, subtract the equations, giving you the result:
1 = 10k
k = 0.1
Then plug k back into one of the equations:
4.80 = c+28(0.1)
c = 4.80-2.80 = 2
Armed with c and k, you can calculate the tip on a bill of $24:
tip = 2+24(0.1) = 2+2.4 = 4.40
Choice (C) is correct.