BlueDragon2010 wrote: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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