Number Properties - DS Rephrasing Example for OG #144

[Guest]

144. If n is a pisitive integer, is (1/10)^n < 0.01?

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

The MGMAT Guide has rephrased this as follows:

Is (1/10)^n < 0.01?

Is (1/10)^n < 1/10

Is n>2?

(1) n > 2
(2)
(1/10)^n x (1/10)^-1 < 1/10 (Step 1)
(1/10)^n x 10 < 1/10 (Step 2)
(1/10)^n < 1/100 (Step 3)
(1/10)^n < 1/10^2 (Step 4)
n>2

For (2), how does the sign in the Step 4 get flipped from < to > when the inequalities rule states that the sign only flips when you multiply/divide by a negative number? Does it have to do something with the numbers being fractions?

[StaceyKoprince]

We could have spelled this one out a bit better.

We're using logic here - knowledge of what happens when a fraction between zero and one is raised to a power. Ordinarily, when we raise something to a power, it gets bigger, but when a fraction between zero and one is raise to a power, it gets smaller.

Here, we have: (1/10)^n < 1/10^2, which is the same thing as: (1/10)^n < (1/10)^2
So, since the first part, raised to the n, is smaller than the second part, raise to the 2, and I know that fractions get smaller as they are raised to higher powers, then n must be greater than 2.

[Greg]

Is the answer D?

[StaceyKoprince]

yep!