Explanation

We know this number k is an integer, and a glance at the statements indicates that we may or may not have a thousands digit. We can imagine the digits each in a spot:



The shaded position is the hundreds digits, which is what we are looking for. On to the statements, separately first.

Statement (1) describes the thousands digit of 10k. For example, if , then . Since multiplying by 10 adds the digit 0 onto a number and shifts the existing digits to the left, then thousands digit of 10k will always equal the hundreds digit of k. Statement (1) therefore gives us sufficient information to answer the question.

Statement (2) tells us about the hundreds digit of k. Again, is a permissible case, because has a hundreds digit of 7. Will the hundreds digit be 7 in all permissible cases? is not a permissible case, because doesn't have a hundreds digit of 7. But along those lines, is a permissible case, because and it does have a hundreds digit of 7. And the legal case k=699 gives a different answer to the question posed. Therefore, Statement (2) does not give us sufficient information to answer the question.

The correct answer is (A).