First post here, so I hope I got the format right. I understand the
OG explanation to this problem, but I tried taking a slightly alternate route and am coming up with the wrong answer. It's a rather simple one, but hope someone can shed some light on to where I've gone wrong. I included the
OG explanation as well as my own in the spoiler.
If \(n\) is a positive integer, is \(\frac{1}{10}^n < 0.01?\)
1) \(n > 2\)
2) \(\frac{1}{10}^{n-1} < 0.1\)
OG Explanation: Manipulate both sides to be expressed as powers of 10.
\(\frac{1}{10}^n < 0.01\)
\((10^{-1})^n < 10^{-2}\)
\(10^{-n} < 10^{-2}\)
\(n > 2\)
1) \(n > 2\). SUFFICIENT2) \(\frac{1}{10}^{n-1} < 0.1\)\((10^{-1})^{n-1} < 10^{-1}\)
\(10^{-n+1} < 10^{-1}\)
\(-n+1 < -1\)
\(n > 2\)
SUFFICIENT
My slightly modified solution for statement 2 was to first manipulate the 0.1 on the right side of the inequality to become a fraction and to leave the left side as a fraction (my first instinct is to see that 0.01 is the same as 1/10). You would have:
\(\frac{1}{10}^{n-1} < \frac{1}{10}^1\)
\(n-1 < 1\)
\(n < 2\)
As you can see, I get an opposite answer. I know this is super simple, but where am I going wrong?
Welcome to GMAT Club. Below is an answer to your question.
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: \((\frac{1}{10})^{2} < (\frac{1}{10})^1\) --> \(2>1\).