A, B, C and D are in Arithmetic Progression, what is the num

The answer depends on whether there are missing brackets in Statement 1. If Statement 1 is supposed to read:

B = (A+C+D)/2

then the answer is A, because if A, B, C are equally spaced, B is always equal to (A+C)/2, so if it is also equal to (A+C+D)/2 = (A+C)/2 + D/2, then certainly D/2 = 0 and D = 0, so the product ABCD is 0. So Statement 1 is sufficient, and Statement 2 clearly is not, and the answer is A.

But if the bracketing is as written, the answer is C. If Statement 1 actually means

B = A + C + (D/2)

then if you replace A, B, C and D respectively with a, a + d, a + 2d and a + 3d, and solve, you'll end up finding that a = (-5/3)d. That's not sufficient, as any two examples will demonstrate. We'd need both Statements to answer the question (Statement 2 tells us d = 2, so we can use that to find a and thus find every term in the sequence, and thus answer any question about the sequence).