Explanation

This question uses factorial notation. , all the way down to 1. So x is that large product plus 11. Let's consider the simplest case from the answer choices, x divided by 11:



If this thing is an integer, than x is divisible by 11. It's equal to



The second term here becomes one. The first one is an integer. In fact, is divisible by every integer from 1 to 100, because it contains all of them as a factor. So is an integer, and x is divisible by 11. Similar logic shows that the other answer choices do not yield integers.

The correct answer is (A).