If n is an integer, is (0.1)^n…
We must determine whether (0.1)^n > (10)^n. We can rephrase the question as:
Is (1/10)^n > (10)^n ?
This can be true only if n is a negative number. For example, if n = -1, then (1/10)^-1 = 10 and (10)^-1 = 1/10. Therefore, this boils down to determining whether n is negative.
Statement One Alone:
n > -10
This doesn’t tell us whether n must be negative. For example, n could be -2 or 2. If it’s the former, then:
(1/10)^-2 > (10)^-2
(10)^2 > (1/10)^2
100 > 1/100
If it’s the latter, then:
(1/10)^2 < (10)^2
1/100 < 100
Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
n < 10
Again this doesn’t tell us whether n must be negative. For example, n could be -2 or 2. Like statement one, the information in statement two is not enough information to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using statements one and two together know that -10< n < 10; however, we still do not have sufficient information to answer the question (again we can use n = 2 and n = -2 to show in one scenario where (1/10)^n > (10)^n while in another (1/10)^n < (10)^n).