If n, m, and p are distinct, five-digit positive integers and if p = n

Official Explanation

To understand this question without going variable-crazy, we can draw a diagram of adding two five-digit numbers with blank spaces, like this,



or whatever helps to visualize the addition. We're being asked whether the digits in the thousands position--the highlighted cells, in this figure--add up independently. Just as we learned in grade school, it boils down to whether we carried a 1 from adding the hundreds digits. If those digits add up to 10 or more, then we'll carry a one and the answer to this question will be "no"; otherwise, it will be "yes." On to the data statements, separately first.

Statement (1) tells us about the wrong column. It's saying nothing about whether the hundreds column will carry over to the thousands. Insufficient.

Statement (2) allows us to determine that there is no carrying of a digit to the thousands column, so we can answer the question definitively (in the affirmative). We have sufficient information.

The correct answer is (B).