At this point, one way we could solve this question by plugging in answer choices. Let's try answer choice A, which is 4.
From here, we can cancel a 2 from the numerator and the denominator, and we are left with:
Here, we cannot do any more cancelling. So we know that k is a fraction—it is not an integer. So thus, A cannot be the answer.
We could continue this process for all the other answer choices, until we find one that creates an integer value for k.
Another possible strategy is to look closely at the prime factorization of 462, and ask ourselves whether we can take one or more of these numbers and use them to create any of our answer choices. Notice that 2 11 = 22. This means that if n = 22 (which is answer choice E), we would have:
Here the 2s and the 11s cancel, leaving us with
So with answer choice D, k is an integer. So (E) must be the right answer.
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