M7MBA wrote:How many integers n are there such that a > n > b ?

(1) a − b = 4
(2) a and b are not integers.

The OA is C.

How can I determine the number of integers between "a" and "b"? I couldn't solve it. Experts, I'd like your help.

Statement 1 -
Case 1: a = 5 and b = 1. The integers between 1 and 5 are: 2, 3, and 4, giving us a total of three integers.
Case 2: a = 5.5 and b = 1.5. The integers between 1.5 and 5.5 are: 2, 3, 4, and 5, giving us a total of four integers.
Because there could be three or four values of n, this statement alone is not sufficient to answer the question.

Statement 2: Clearly not sufficient. You could have a = .5 and b = 2.5, or a = .5 and b = 100.5, etc . There's an infinite number of possibilities here.

Together: We can reuse Case 2 from statement 1, as 5.5 and 1.5 are not integers. We can continue to pick numbers, but you'll quickly see that no matter what we pick, there will always be four integers between 'a' and 'b.' Because there is only one possible value that satisfies the conditions, the two statements together are sufficient, and the answer is C.