If n is a positive integer, what…
We are given that n is a positive integer, and we must determine the tens digit of n.
Statement One Alone:
The hundreds digit of 10n is 6.
In order for the hundreds digit of 10n to be 6, the tens digit of n must be 6.
For example, if n = 60, then 10n = 600; and if n = 169, 10n =1,690.
We see that whenever we multiply a positive integer (at least two digits) by 10, the original tens digit will be the hundreds digit of the resulting integer. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
If you are wondering why n has to be at least two digits, note that if n is only one digit, such as n = 7, there will be no hundreds digit when we multiply 7 by 10 to get 70. Statement one specifically states that the hundreds digit of 10n is 6, so we can ignore all single-digit numbers in our consideration.
Statement Two Alone:
The tens digit of n+1 is 7.
Using the information in statement two we see that n could have a tens digit of 6 (for example, n = 69) or n could also have a tens digit of 7 (for example, n = 70). Thus, statement two is not sufficient to answer the question.