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Let’s look at (1):
What numbers have exactly 2 positive factors? Well, we know 2 has factors: 1 and 2.
Are there any other numbers?
What about 3? 3 has factors: 1 and 3.
So here we have two different possibilities to the question: is n equal to 2?
Because of this ambiguity, we know (1) is no good, so the answer is either (B), (C), or (E).

Now, let’s take a look at (2):
—the keyword in Statement #2 is “ANY”–always be careful when you see absolute words like this.
Say you pick 10 as you did. Factors of 10: 1, 2, 5, 10
The difference between ANY positive factor of n must be odd to satisfy requirement #2.
Well, 10-1= 9 = odd
And yes, 5-2 = 3 = odd
And yes, 2-1 = 1 = odd
and yes, 10 – 5 = 5 = odd

BUT

5-1 = 4 = even
10 – 2 = 8 = even

The keyword ANY makes it extremely difficult to find a number that satisfies statement #2. And the more factors a number has, the more difficult it is. Only with a super small number that only has 2 factors (like the number 2) might this work. Let’s look:
#2: 1, 2
2-1 = 1 = odd

what about 3?
#3: 1, 3
3-1 = 2 = even..

The number must be 2 using statement #2 alone so answer is B. Be wary of words like “any.”

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First you should rephrase the question as I do in Framework #1.

Let’s look at statement #1. What happens when n=2? You should recognize that
if n=2, then the inequality is equal on both sides.
(1/10)^2 = .01 —— so then you get “Is .01< .01?"
You should recognize two points:

1) And you should recognize that as n gets bigger, then we have
a true statement.

2) If n gets smaller, then we get a false statement.

In other words, you can “translate” the ORIGINAL question to asking:
“Is n >2?”

Statement (1) tells us, YES! — [ n > 2 ] —so we know (1) alone is good.

With statement #2, see if you can simplify what statement #2 is saying.
Try values for n: 1, 2, and 3

Try n=1
(1/10) ^ 0 = 1 [anything to the zero power=1]
Continue looking at statement #2 (not the original question yet):
Is 1<.1? No. That means n cannot = 1. Keep that in mind.

Try n=2
(1/10) ^ (1) <.1
Continue looking at statement #2 (not the original question yet):
Is .1<.1? No, they're the same so we're right at the border. That means n cannot = 2

Try n=3
(1/10) ^ 2 < .1
Is .01 < .1? Yes! That means n can = 3

And the higher n is the more this will be true.
So in other words, statement (2) is saying n >2–which is
exactly what statement (1) is saying.

They’re saying the same thing! And we already know (1)
is good–I’m assuming you got 1 as good?
So that means (1) is good, (2) is good –> answer is (D).

So as you say if n is less than 3, then statement (2) is not satisfied so
we can’t pick n less than 3.
Remember you must pick values of n so that the requirements
are satisfied. Once you do that, THEN you answer the question which we
translated before as: “Is n>2?”

To A Higher GMAT Score,