questioner wrote:

Not sure I am following the logic here due to the fact that Answer Choice E seems to be larger than Answer Choice D? I could be completely missing the point here, and most likely the case, but if you have some additional explanation that would be really helpful. Would picking numbers at all make sense here? Also, is this a 700-800 level question or more in the range of 600-700?

This is more a 600-700 question, though it might look harder. But the concept is very simple:

1. The smallest possible number, which is divisible by both 2ª and 3²ª is 2ª × 3²ª .

2. Choice E, 6²ª , is greater than 2ª × 3²ª , so it is definitely NOT a divisor of 2ª × 3²ª.

We have shown that at least one possible value of

*n* (2ª × 3²ª) is NOT divisible by E. So E might NOT be a divisor of

*n*.

The question tests the following abilities:

- dealing with powers

- knowing what factorization is and how it is connected to divisibility.

**ANOTHER APPROACH**.

Take a look at the answer choices. Exactly one of them must be the correct answer.

Choice E is divisible by any other answer choice. So if E is a divisor of

*n*, then all the other answer choices are divisors as well.

Thus E cannot be the divisor of all possible values of

*n*, because in this case all the answer choices would be the divisors and we would have NO correct answer.

A. 6

B. 3 × 2ª

C. 2 × 3²ª

D. 6ª

E. 6²ª