I think the question means to refer to the 'tenths' digit and the 'hundredths' digit, because 1/n does not have a 'tens digit' or 'hundreds digit' if n is a positive integer.

Going with that assumption, I don't see how we can do this question without looking at decimal expansions.

AleksandrM wrote:I will have to go with E.

If n is less than 10, then 1/n could be 1/9 = 1 in tens digit or 1/4 = 2 in the tens digit.

Same goes for 1/n for the second statement 1/2 = 0 in hundreds digit and 1/8 = 2 in the hundreds digit.

The logic above is incorrect; n cannot be 9, because the tenths digit of 1/9 is equal to 1, not 9. Let's look at what values n might have:

1) If n = the tenths digit of 1/n, then n cannot be 1 or 2, but n might be 3. But as you make n larger than 3, the tenths digit of 1/n gets smaller: it's equal to either 1 or 2, depending on n. So the tenths digit of 1/n is only equal to n when n=3; sufficient.

2) If n = the hundredths digit of 1/n, we have more work to do. Certainly, n might be equal to 3, since 1/3 = 0.3333..... But, as we check the other decimal expansions, we discover that n might be equal to 6, since 1/6 = 0.166666.... So we have more than one choice for n: insufficient.

A.