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

 It is currently 24 Oct 2016, 11:25

# GMAT Club Live:

9 most common EMBA mistakes

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

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

Kudos [?]: 13 [3] , given: 0

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

### Show Tags

16 Mar 2012, 10:04
3
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (02:06) correct 29% (01:13) wrong based on 1030 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 35275
Followers: 6636

Kudos [?]: 85555 [1] , given: 10237

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

### Show Tags

16 Mar 2012, 10:32
1
KUDOS
Expert's post
6
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?

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.
_________________
Intern
Joined: 15 Mar 2012
Posts: 4
Followers: 0

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

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

### Show Tags

16 Mar 2012, 17:07
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
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 30 [0], given: 17

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

### Show Tags

09 Aug 2012, 01:08
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.
Math Expert
Joined: 02 Sep 2009
Posts: 35275
Followers: 6636

Kudos [?]: 85555 [4] , given: 10237

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

### Show Tags

09 Aug 2012, 01:34
4
KUDOS
Expert's post
8
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.

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.
_________________
Senior Manager
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 21

Kudos [?]: 305 [1] , given: 73

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

### Show Tags

15 Mar 2013, 09:59
1
KUDOS
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

I am still on all gmat forums. msg me if you want to ask me smth

Intern
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]

### Show Tags

18 Mar 2013, 13:13
Great explanation Bunuel, thanks.
Intern
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]

### Show Tags

22 Dec 2013, 00:18
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 qn. is why is it necassary to change the sign to make n> 2??
Math Expert
Joined: 02 Sep 2009
Posts: 35275
Followers: 6636

Kudos [?]: 85555 [0], given: 10237

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

### Show Tags

22 Dec 2013, 04:48
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 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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12211
Followers: 541

Kudos [?]: 151 [0], given: 0

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

### Show Tags

13 Jan 2015, 20:40
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7711
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 343

Kudos [?]: 2282 [0], given: 162

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

### Show Tags

13 Jan 2015, 20:52
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

[Reveal] Spoiler:
D

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

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 23 Sep 2014 Posts: 22 Location: India Concentration: Marketing, Finance GMAT Date: 01-17-2015 Followers: 1 Kudos [?]: 20 [0], given: 148 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 28 Apr 2015, 00:38 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. Would hope to have a reasoning which can clarify where i am going wrong. TIA Math Forum Moderator Joined: 06 Jul 2014 Posts: 1274 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Followers: 135 Kudos [?]: 1641 [2] , given: 178 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 28 Apr 2015, 00:51 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. 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 $$3$$ _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 350 Followers: 112 Kudos [?]: 885 [1] , given: 84 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 28 Apr 2015, 01:04 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. 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. 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 _________________ | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Intern Joined: 23 Sep 2014 Posts: 22 Location: India Concentration: Marketing, Finance GMAT Date: 01-17-2015 Followers: 1 Kudos [?]: 20 [0], given: 148 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 28 Apr 2015, 02:57 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. 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! GMAT Club Legend Joined: 09 Sep 2013 Posts: 12211 Followers: 541 Kudos [?]: 151 [0], given: 0 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 30 Apr 2016, 13:45 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. _________________ Senior Manager Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 331 Location: United States (CA) Followers: 8 Kudos [?]: 77 [0], given: 0 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 14 May 2016, 07:47 Here is my take: We are given that n is a positive integer and need to determine whether (1/10)^n < 0.01. We can convert 0.01 to a fraction and display the question as: Is (1/10)^n < 1/100 ? Is (1/10)^n < (1/10)^2 ? Using the negative exponent rule, we can take the reciprocal of our bases and switch the signs of the exponents. Is 10^-n < 10^-2 ? Because the bases are now the same, we equate the exponents. Is -n < -2 ? Is n > 2 ? Statement One Alone: n > 2 We see that statement one directly answers the question. We can eliminate answer choices B, C, and E. Statement Two Alone: (1/10)^(n-1) < 0.1 We can simplify the inequality in statement two. (1/10)^(n-1) < 0.1 (1/10)^(n-1) < (1/10)^1 Using the negative exponent rule, we can take the reciprocal of our bases and switch the signs of the exponents. 10^-(n-1) < 10^-1 The bases are now equal, so we can equate the exponents. -(n – 1) < -1 n – 1 > 1 n > 2 We see that n is greater than 2. Statement two alone is sufficient to answer the question. Answer: D _________________ Jeffrey Miller Scott Woodbury-Stewart Founder and CEO Intern Joined: 28 Apr 2016 Posts: 48 Followers: 0 Kudos [?]: 1 [0], given: 60 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 24 Aug 2016, 09:26 I had a somewhat similar approach for statement 2, but I landed up with an answer contradicting 1. I considered 0.1 as 1/10 so then the equation is: n-1 < 1 (because the base is the same i.e. 1/10) therefore n < 2...where am I going wrong? Bunuel wrote: pavanpuneet wrote: 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 7711 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 343 Kudos [?]: 2282 [0], given: 162 Re: If n is a positive integer, is (1/10)^n < 0.01? [#permalink] ### Show Tags 24 Aug 2016, 14:11 Hi ameyaprabhu, If you choose to 'convert' the numbers into decimals, then that's fine, but you still have to remember how the rules of math 'work' Which number is bigger: (1/10)^1 or (1/10)^2? WHY is that the case? Since we're working with an inequality, we're bound by the rule that one value MUST be bigger than the other. If you're ever unsure about an 'algebraic' approach that you're using, you can easily verify whether you're correct or not by TESTing VALUES. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 01 Sep 2016
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 12

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

### Show Tags

23 Sep 2016, 11:03
Here is how I solved this question
The question stem states that[b] (1/10))^n<0.01
(1/10)^n < (1/10)^2
Cross multiplying, we get
(10)^2< 10^n
The above expression is possible only when n is greater than 2
Therefore our question becomes: Is n>2 ?

Statement 1: n>2 Sufficient
Statement 2: (1/10)^n-1< 0.1
(1/10)^n-1< 1/10
10< 10^n-1
10< 10^n/10
Cross multiplying, we get
10^2< 10^n
Therefore, n>2

I hope my approach is correct.
Re: If n is a positive integer, is (1/10)^n < 0.01?   [#permalink] 23 Sep 2016, 11:03
Similar topics Replies Last post
Similar
Topics:
4 If n is an integer, is 10^n ≤ 0.001 ? 7 20 Jan 2012, 12:35
3 If m and n are positive integers, is m^n < n^m ? 10 30 Sep 2011, 05:34
4 If n is a positive integer, is ( 1/10 )^n < .01 ? 9 19 Jul 2011, 08:26
14 If m and n are positive integers, is m^n < n^m? 18 22 Sep 2010, 13:37
If n is a positive integer, is (1/10)^n < .01? 14 23 Jun 2008, 00:17
Display posts from previous: Sort by