is (1/10)^n < 0.01?

[BlueDragon2010]

If n is a positive integer, is (1/10)^n < 0.01?

1) n > 2
2) (1/10)^(n-1) < 0.1

[Patrick_GMATFix]

This sentence tests your understanding of how powers of positive fractions work. Remember that within positive fractions, increasing the power decreases the value. The full solution below is taken from the GMATFix App.



-Patrick

[GMATGuruNY]

If n is a positive integer, is (1/10)^n < 0.01?

1) n > 2
2) (1/10)^(n-1) < 0.1

Question stem, rephrased:
Is (1/10)^n < 1/100?

Statement 1: n>2
If n=3, then (1/10)^n = (1/10)³ = 1/1000, which is less than 1/100.
If n=4, then (1/10)^n = (1/10)� = 1/10000, which is less than 1/100.
As the value of n INCREASES, the value of (1/10)^n DECREASES.
Thus, in every case, it will be true that (1/10)^n < 1/100.
SUFFICIENT.

Statement 2: (1/10)^(n-1) < 1/10
If n=1, then (1/10)^(n-1) = (1/10)� = 1, which is NOT less than 1/10.
Thus, it is not possible that n=1.
If n=2, then (1/10)^(n-1) = (1/10)¹ = 1/10, which is NOT less than 1/10.
Thus, it is not possible that n=2.
Implication:
n>2.
As we saw in statement 1, if n>2, then (1/10)^n < 1/100.
SUFFICIENT.

The correct answer is D.

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Hi BlueDragon2010,

Sometimes the best way to tackle a Quant question (whether it's PS or DS) is to just write down all of the possibilities so that you can see the entire situation (and deduce whatever pattern might be hidden within the "math").

Here, we're asked "is (1/10)^N < .01?" This is YES/NO question. We're told that N is a POSITIVE INTEGER

Before dealing with the information in Fact 1, I'm going to do a quick series of minor calculations to see what pattern exists in this situation:

If N = 1, then (1/10)^1 = .1
If N = 2, then (1/10)^2 = 1/100 = .01
If N = 3, then (1/10)^3 = 1/1000 = .001
Etc.

So, the pattern is that as N gets bigger, more zeros appear between the decimal point and the 1.

In reference to the original question, we're essentially asked if N is less than, equal to, or greater than 2.

Fact 1: N > 2
So, N must be greater than 2 (it could be 3, 4, 5, etc.)

Each of those values would create more zeroes between the decimal point and the 1.
N = 3 gives us .001
N = 4 would be smaller and so on.
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: (1/10)^(N-1) < 0.1

While this might be "scary looking", it's based on the same pattern as before (we just need to adjust the math a bit)
N = 1 gives us 1
N = 2 gives us .1
N = 3 gives us .01
N = 4 gives us .001
Etc.

The information in Fact 2 tells us that N MUST be 3 or greater. This is the SAME information as what we had in Fact 1.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich