Data Sufficiency

pemdas wrote:
you committed the typical inequality error -> taking reciprocals reverses the sign

I don't recommend learning rules for inequalities and reciprocals, because they aren't entirely straightforward. You can always just multiply and divide on both sides of your inequality to get the same result, so you don't need to learn any rules for reciprocation. It is true that you need to reverse your inequality if you take reciprocals on both sides *if* all the quantities involved are positive. For example, if we have this inequality, which is clearly true:

1/3 < 1/2

then when we take reciprocals on both sides, we need to reverse the inequality to get something which is true:

3 > 2.

That is *not* the case if you have a negative quantity in one of your fractions. For example, this inequality is clearly true:

-1/2 < 1/3

but if we take reciprocals on both sides, we do *not* want to reverse the inequality:

-2 < 3

Using rules for inequalities and reciprocals is especially dangerous when you have unknowns. For example, if you have the inequality:

2/x < 3/y

you certainly cannot take reciprocals on both sides and reverse the inequality *unless* you know that x and y are both positive (or both negative). In such situations, I find it safer not to use reciprocal rules at all. Instead I will try to multiply on both sides by x and by y, which will remind me that I need to know the signs of x and y to proceed.

barrelbowl wrote:
Originally I rephrased the question as is (1/10)^n < (1/10)^2 or is n < 2?

What you've done here would be correct if your base was a positive integer. You can get a positive integer base here, since 1/10 is just equal to 10^(-1). So you can rewrite the question as follows:

(1/10)^n < (1/10)^2
10^(-n) < 10^(-2)
-n < -2
n > 2

(in the last step, we reverse the inequality since we multiplied by -1 on both sides)