Explanation

The question is not so complicated, especially if we consider a case. If and , for example, we are talking about the number of integers from 1 to 10, including 1 and 10. In that case, the answer would be 10. Let's take a look at the data statements, separately first.

Statement (1) tells us the difference between the integers. This is not the same as the answer to the question asked, but it gives us the answer to the question asked--it's just 1 more. For example, the difference between 1 and 23 is 22, and the number of integers from 1 to 23, inclusive, is 23. Sufficient.

Statement (2), like Statement (1), tells us something that is not exactly the answer to the question, but which definitively gives us the answer. If there are 21 integers between, but not including, i+1 and k+1, then we bring this interval one notch left on the number line, and there are 21 integers between, but not including, i and k. Then, including i and k throws in two more integers, so the total number inclusive is 23. Sufficient.

The answer is (D).