If n is a Positive Integer, is \((\frac{1}{10})^{n}<0.01\)? GMAT Data Sufficiency

Question: If n is a positive integer, is \((\frac{1}{10})^{n}<0.01\)?

1. n > 2
2. \((\frac{1}{10})^{n-1}<0.1\)

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If n is a positive integer, is \((\frac{1}{10})^{n}<0.01\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach Solution (1):

If you have a problem with fractions in powers, then manipulate to get rid of them:

\((\frac{1}{10})^{n-1}<\frac{1}{10}\to\frac{1}{10^{n-1}}<\frac{1}{10}\)

Cross multiply:

\(10 <10 ^{n-1} \rightarrow 1 < n-1 \rightarrow n > 2\)

OR

\((\frac{1}{10})^{n-1}<\frac{1}{10}\to({10^{-1}})^{n-1}<{10^{-1}}\to10^{1-n}<10^{-1}\to1-n<-1\to n<2\)

Correct Answer: D

Approach Solution (2):

From \((\frac{1}{10})^{n-1}<(\frac{1}{10})^{1}\) since the base, 1/10, is a fraction in the range (0,1) then it should be n – 1 > 1. For example:\((\frac{1}{10})^{2}<(\frac{1}{10})^{1}\to2>1\)

Correct Answer: D

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