Given:
y = (C - B)/A

Statement 1: C - B > 0
which only tells that the numerator of 'y' is positive. Depending on the value of A, y can hold many values.

Statement 2: A > 0
this talks about only the denominator. Based on the values of B and C, y can hold many values.
There is no way (B) could be the correct option.

Let's try to combine the two statements.
Now, y = (positive quantity)/(A quantity greater than 1)

Again, 'y' can hold many values. The question doesn't even say that 'y' has to be an integer.

No conclusive answer. (E) should be correct.

How many different numbers y are there such that Ay + B = C (A, B, and C are known) ?

The question states that the value of y = (C-B)/A. So, if the value of A is not equal to zero, we can say that y =(C-B)/A, a single value. If the value of A is zero, the value of y is undefined and there are infinite/No numbers in the number system that satisfy the equation.

1. C > B

The statement doesn't speak of A or its value, hence the statement is insufficient to answer the question.

2. A > 1

If the value of A is greater than 1, then we know that A is definitely not equal to 0. So, The value of y = (C-B)/A and y has just one value. Therefore the statement is sufficient to answer the question.

IMO B

I agree with the analysis above.
I didn't note that the values of A,B and C are known, and that's the catch.