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If n is a positive integer, is (1/10)^n < 0.01?

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If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 16 Mar 2012, 09:04
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If n is a positive integer, is \frac{1}{10}^n < 0.01?

(1) n > 2

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

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.

[Reveal] Spoiler:
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. SUFFICIENT


2) \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?
[Reveal] Spoiler: OA
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 16 Mar 2012, 09:32
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tkaelle wrote:
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. SUFFICIENT


2) \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.

Hope it helps.
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 16 Mar 2012, 16:07
Thanks for the quick response. I knew that you had to switch the inequality sign if you were multiplying or dividing by a negative value, but the same is also true when working with a value 0 < x < 1?

I'm a little confused because in this case, we're not doing any multiplying or dividing to the equation, but just ignoring the common base and comparing their exponents. Not quite sure why we change the sign :(
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 09 Aug 2012, 00:08
Hi Bunuel,

I actually landed up doing in the exact same way as tkaelle did. I understand what you mentioned .. however, is there any rule because I am sure I might up land up doing the same in the exam if I do not understand why we switch the signs/ or why cant we manipulate the fraction 1/10 and continue?

Thank you.
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 09 Aug 2012, 00:34
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pavanpuneet wrote:
Hi Bunuel,

I actually landed up doing in the exact same way as tkaelle did. I understand what you mentioned .. however, is there any rule because I am sure I might up land up doing the same in the exam if I do not understand why we switch the signs/ or why cant we manipulate the fraction 1/10 and continue?

Thank you.


It's not about switching sign.

If you have a problem with fractions in powers, then manipulate to get rid of the them:
(\frac{1}{10})^{n-1} < \frac{1}{10} --> \frac{1}{10^{n-1}}< \frac{1}{10} --> cross-multiply: 10<10^{n-1} --> 1<n-1 --> n>2.

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

Hope it helps.
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 15 Mar 2013, 08:59
given 10^(-n)<10^(-2)
n>2 ?


1) n>2 suff

2) 10^(1-n)<10^(-1)
1-n<-1
n>2 suff

ans is D
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 18 Mar 2013, 12:13
Great explanation Bunuel, thanks.
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 21 Dec 2013, 23:18
Hi !

I have an issue with the 2nd equation :

(1/10)^n-1 < 0.1

What I would do is (1/10)^n-1 < 1/10)

n-1 < 1
My answer :n<2

My qn. is why is it necassary to change the sign to make n> 2??
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Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 22 Dec 2013, 03:48
Expert's post
mba1010 wrote:
Hi !

I have an issue with the 2nd equation :

(1/10)^n-1 < 0.1

What I would do is (1/10)^n-1 < 1/10)

n-1 < 1
My answer :n<2

My qn. is why is it necassary to change the sign to make n> 2??


Please check here: if-n-is-a-positive-integer-is-1-10-n-129176.html#p1059737 and here: if-n-is-a-positive-integer-is-1-10-n-129176.html#p1111563

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If n is a positive integer, is (1/10)^n < 0.01?   [#permalink] 22 Dec 2013, 03:48
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