Find all School-related info fast with the new School-Specific MBA Forum

It is currently 06 May 2015, 17:20

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
avatar
Joined: 15 Mar 2012
Posts: 4
Followers: 0

Kudos [?]: 4 [2] , given: 0

If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 16 Mar 2012, 09:04
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (02:02) correct 31% (01:19) wrong based on 501 sessions
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
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27238
Followers: 4237

Kudos [?]: 41161 [3] , given: 5672

Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 16 Mar 2012, 09:32
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 15 Mar 2012
Posts: 4
Followers: 0

Kudos [?]: 4 [0], given: 0

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 :(
Manager
Manager
avatar
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 13 [0], given: 17

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.
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27238
Followers: 4237

Kudos [?]: 41161 [2] , given: 5672

Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 09 Aug 2012, 00:34
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Current Student
User avatar
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 15

Kudos [?]: 187 [0], given: 73

GMAT ToolKit User
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
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

Intern
Intern
avatar
Joined: 12 Mar 2013
Posts: 4
Followers: 1

Kudos [?]: 0 [0], given: 7

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.
Intern
Intern
avatar
Joined: 29 Aug 2013
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 0

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??
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27238
Followers: 4237

Kudos [?]: 41161 [0], given: 5672

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4790
Followers: 296

Kudos [?]: 52 [0], given: 0

Premium Member
Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 13 Jan 2015, 19:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1898
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 79

Kudos [?]: 502 [0], given: 38

Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 13 Jan 2015, 19:52
Expert's post
Hi All,

This DS question is essentially about arithmetic rules (decimals and exponents). It can be solved conceptually or you solve it by TESTing VALUES.

We're told that N is a POSITIVE INTEGER. We're asked (1/10)^N < 0.01 This is a YES/NO question

Fact 1: N > 2

IF....
N = 3
(1/10)^3 = 1/1000 = .001 and the answer to the question is YES

N = 4
(1/10)^4 = 1/10,000 = .0001 and the answer to the question is YES

As N gets bigger, the resulting decimal point gets smaller and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: (1/10)^(N-1) < 0.1

Here, we have an interesting "restriction" - we can only use certain values for N....

IF....
N = 1
(1/10)^0 = 1 BUT this does NOT fit with the given information in Fact 2, so we CANNOT use this TEST CASE.

IF....
N = 2
(1/10)^1 = .1 BUT this also does NOT fit with the given information in Fact 2 EITHER.

This means that N CANNOT be 1 or 2. Since it has to be a POSITIVE INTEGER and we already have proof of what happens when N > 2 (the answer to the question is ALWAYS YES), we can stop working.
Fact 2 is SUFFICIENT

Final Answer:
[Reveal] Spoiler:
D


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts
http://gmatclub.com/blog/courses/empowergmat-discount/?fl=menu

Image

Intern
Intern
avatar
Joined: 23 Sep 2014
Posts: 11
Location: India
Concentration: Marketing, Finance
GMAT Date: 01-17-2015
Followers: 0

Kudos [?]: 9 [0], given: 40

If n is a positive integer, is (1/10)^n < 0.01? [#permalink] New post 27 Apr 2015, 23:38
The question says that n is any positive number.

So when I use n=2 in the second statement then both the equations become equal and the equality fails i.e 0.1<0.1 doesn't hold,

Similarly when i use n=1, then 1<0.1 again a different answer
and when n=3, then it satisfies.

So how come answer is D??

I know i am doing something wrong. :x

Would hope to have a reasoning which can clarify where i am going wrong.

TIA
2 KUDOS received
Math Forum Moderator
User avatar
Joined: 06 Jul 2014
Posts: 206
Location: Ukraine
Followers: 4

Kudos [?]: 115 [2] , given: 53

GMAT ToolKit User Premium Member CAT Tests
here is an OG problem in which i have a real doubt in [#permalink] New post 27 Apr 2015, 23:51
2
This post received
KUDOS
believer700 wrote:
The question says that n is any positive number.

So when I use n=1 in the second statement then both the equations become equal and the equality fails i.e 0.1<0.1 doesn't hold.

So how come answer is D??

I know i am doing something wrong. :x

Would hope to have a reasoning which can clarify where i am going wrong.

TIA


Hello believer700

You should use information not only from task but from statement too.
When you use \(n = 1\) you break condition of second statement \((\frac{1}{10})^{(n-1)} <0.1\) and this mean that you can't use such value for \(n\)
So you should combine conditions from task and statement.

This mean that you can take only those values for \(n\) that will satisfy condition of task and statement.

So when \(n = 1\) then it will be \((\frac{1}{10})^{(1-1)} <0.1\); \(\frac{1}{1}<0.1\); not possible

when \(n = 2\) then it will be \((\frac{1}{10})^{(2-1)} <0.1\); \(\frac{1}{10}<0.1\); not possible

when \(n = 3\) then it will be \((\frac{1}{10})^{(3-1)} <0.1\); \(\frac{1}{10}<0.1\); possible
So \(n\) should be at least \(3\)
Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
Joined: 04 Jan 2015
Posts: 128
Followers: 16

Kudos [?]: 117 [1] , given: 28

Re: here is an OG problem in which i have a real doubt in [#permalink] New post 28 Apr 2015, 00:04
1
This post received
KUDOS
Expert's post
believer700 wrote:
The question says that n is any positive number.

So when I use n=2 in the second statement then both the equations become equal and the equality fails i.e 0.1<0.1 doesn't hold,

Similarly when i use n=1, then 1<0.1 again a different answer
and when n=3, then it satisfies.

So how come answer is D??

I know i am doing something wrong. :x

Would hope to have a reasoning which can clarify where i am going wrong.

TIA


Dear believer700

It's good that you're being inquisitive about your mistakes. Analyzing the mistake you make once ensures that you don't ever make it again. :-D

The part that you did wrong here that you considered only one piece of information about n: that n is a positive integer (this is given in the ques statement)

So, you thought that you could take n = 1 or 2. And then, got confused when these values of n did not satisfy the information given in Statements 1 and 2.

The correct way of talking about n is:

n is a positive integer such that (1/10)^(n-1) <0. (info in St. 2)

OR

n is a positive integer such that n > 2 (info in St. 1)

So, the possible values of n will be those that satisfy:

i) The information given in question statement AND
ii) The information given in Statements 1 and 2

I hope this clarifies your doubt! :)

- Japinder
_________________

Image

Intern
Intern
avatar
Joined: 23 Sep 2014
Posts: 11
Location: India
Concentration: Marketing, Finance
GMAT Date: 01-17-2015
Followers: 0

Kudos [?]: 9 [0], given: 40

Re: here is an OG problem in which i have a real doubt in [#permalink] New post 28 Apr 2015, 01:57
Harley1980 wrote:
believer700 wrote:
The question says that n is any positive number.

So when I use n=1 in the second statement then both the equations become equal and the equality fails i.e 0.1<0.1 doesn't hold.

So how come answer is D??

I know i am doing something wrong. :x

Would hope to have a reasoning which can clarify where i am going wrong.

TIA


Hello believer700

You should use information not only from task but from statement too.
When you use \(n = 1\) you break condition of second statement \((\frac{1}{10})^{(n-1)} <0.1\) and this mean that you can't use such value for \(n\)
So you should combine conditions from task and statement.

This mean that you can take only those values for \(n\) that will satisfy condition of task and statement.

So when \(n = 1\) then it will be \((\frac{1}{10})^{(1-1)} <0.1\); \(\frac{1}{1}<0.1\); not possible

when \(n = 2\) then it will be \((\frac{1}{10})^{(2-1)} <0.1\); \(\frac{1}{10}<0.1\); not possible

when \(n = 3\) then it will be \((\frac{1}{10})^{(3-1)} <0.1\); \(\frac{1}{10}<0.1\); possible
So \(n\) should be at least \(3\)


Thanks for the Explanation!!
Did not concentrate enough! :(
Re: here is an OG problem in which i have a real doubt in   [#permalink] 28 Apr 2015, 01:57
    Similar topics Author Replies Last post
Similar
Topics:
1 If n is a positive integer, is ( 1/10 )^n < .01 ? 386390 6 19 Jul 2011, 07:26
If n is a positive integer, is (1/10)^n < .01? redbeanaddict 14 22 Jun 2008, 23:17
If n is a positive integer, is (1/10)^n < 0.01? (1) n lumone 1 13 Jan 2008, 07:32
If n is a positive integer, is (1/10)^n less than 0.01? (1) above720 1 23 Aug 2007, 17:50
If n is a positive integer is (1/10)^n < 0.01? I) n > scorpioguy 2 06 Nov 2005, 17:23
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.