# If n is an integer, is (0.1)^n…

# Solution:

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).

**Answer: E **