Question

If $n$ is a positive integer, is $(\frac{1}{10}{)}^n<0.01$?
(1) $n>2$
(2) $(\frac{1}{10}{)}^{n-1}<0.1$

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

We will express both sides as power of 10 to simplify the question.

LHS:

$(0.1{)}^n$ $\to$ ${10}^{-n}$

RHS:

$0.01\to$ ${10}^{-2}$

$n>2$

1st is sufficient.

${10}^{1-n}$$<$${10}^{-1}$

$n>2$

This is also sufficient.

Hence, Option D is correct.