Problem 2

If y is an integer and y³ - 4y = 48, what is y² + 4?

(A) 29
(B) 24
(C) 20
(D) 16
(E) 13

Let's start by factoring the left side of y³ - 4y = 48. We have y³ - 4y = y(y² - 4) = y(y-2)(y+2). If we rearrange terms a little, it is (y-2)y(y+2) = 48

Notice that y-2, y, and y+2
must be either three consecutive even integers, or three consecutive
odd integers. Since the product, 48, is even, these must be three
consecutive even integers. So we
need to find three consecutive even integers whose product is 48. If
you experiment a little, you should come up with 2?4?6 = 48, and
therefore, y = 4.

4² + 4 = 20, so the correct answer is C.