GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 23:34 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If n is an integer, is (0.1)^n greater than (10)^n?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58445
If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
29 00:00

Difficulty:   5% (low)

Question Stats: 82% (01:23) correct 18% (01:31) wrong based on 1370 sessions

HideShow timer Statistics

If n is an integer, is $$(0.1)^n$$ greater than $$(10)^n$$?

(1) $$n > -10$$

(2) $$n < 10$$

Kudos for a correct solution.

_________________

Originally posted by Bunuel on 25 Oct 2015, 09:01.
Last edited by carcass on 21 Jul 2018, 14:19, edited 2 times in total.
Edited by Carcass
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

15
3
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Question : is (0.1)^n > (10)^n?
Question : is (1/10)^n > (10)^n?
Question : is (10)^{-n} > (10)^n?
Question : is (-n) > n?
Question : is (2n) < 0?

Question : is n < 0?

Statement 1: n > −10
n may be Negative or Positive. Hence
NOT SUFFICIENT

Statement 2: n < 10
n may be Negative or Positive. Hence
NOT SUFFICIENT

Combining the two statements
even after combining the two
-10 < n < 10
i.e. n may be Negative or Positive. Hence
NOT SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
CEO  S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

9
1
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Is (0.1)^n > (10)^n ---> $$10^{-n} > 10^n$$ ---> $$10^{2n} < 1$$ ---> $$10^{2n} < 10^0$$ ---> 2n < 0 ---> is n<0?

Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient.

Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient.

Combining, the above 2 cases still apply giving you an ambiguous answer.

Thus, E is the correct answer.
General Discussion
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

6
4
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Target question: Is (0.1)^n greater than (10)^n?

REPHRASED target question: Is (1/10)^n greater than (10)^n?

Statement 1: n > −10
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 1, in which case (1/10)^n is NOT greater than (10)^n
Case b: n = -1, in which case (1/10)^-1 = 10 and 10^-1 = 1/10. Here, (1/10)^n IS greater than (10)^n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: n < 10
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 1, in which case (1/10)^n is NOT greater than (10)^n
Case b: n = -1, in which case (1/10)^-1 = 10 and 10^-1 = 1/10. Here, (1/10)^n IS greater than (10)^n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

IMPORTANT - Notice that I tested the SAME VALUES for both statements. This means that, the STATEMENTS COMBINED are also NOT SUFFICIENT

Cheers,
Brent
_________________
Manager  Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04-01-2015
GPA: 3.98
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

2
1
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Sol. (10)^-n > (10)^n or -n>n or n<0 ?
1) n > -10 Not sufficient
2) n < 10 Not sufficient

1) + 2) -10 < n <10 Not sufficient

Hence E
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks
Manager  D
Joined: 17 May 2015
Posts: 246
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
Please note that for n=0, both the expressions will be equal to 1.

Intern  S
Joined: 10 Jun 2016
Posts: 45
Schools: IIM-A"19
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Hello All,

Got tricked by the question, finally got it

S-1) If n = -9 then Yes as (0.1)^-9 > 10^-9. But Not true of n = 9. Not Sufficient as we dont know value of n.
S-2) Same info as S-1 in different way. So If n = -9 Yes. n = 9 its not sufficient.
_________________
Thank You Very Much,
CoolKl
Success is the Journey from Knowing to Doing

A Kudo is a gesture, to express the effort helped. Thanks for your Kudos.
Intern  B
Joined: 22 Jan 2017
Posts: 5
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Would one way to solve this question to log expressions so you end up with n*log(0.1) and n*log(10) and then trying range of values?
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Engr2012 wrote:
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Is (0.1)^n > (10)^n ---> $$10^{-n} > 10^n$$ ---> $$10^{2n} < 1$$ ---> $$10^{2n} < 10^0$$ ---> 2n < 0 ---> is n<0?

Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient.

Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient.

Combining, the above 2 cases still apply giving you an ambiguous answer.

Thus, E is the correct answer.

how do you get 10^(2n) <1 from $$10^{-n} > 10^n$$
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Engr2012 wrote:
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Is (0.1)^n > (10)^n ---> $$10^{-n} > 10^n$$ ---> $$10^{2n} < 1$$ ---> $$10^{2n} < 10^0$$ ---> 2n < 0 ---> is n<0?

Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient.

Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient.

Combining, the above 2 cases still apply giving you an ambiguous answer.

Thus, E is the correct answer.

How do you get $$10^{2n} < 1$$ from $$10^{-n} > 10^n$$
Intern  B
Joined: 09 Dec 2014
Posts: 37
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
pclawong wrote:
Engr2012 wrote:
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Is (0.1)^n > (10)^n ---> $$10^{-n} > 10^n$$ ---> $$10^{2n} < 1$$ ---> $$10^{2n} < 10^0$$ ---> 2n < 0 ---> is n<0?

Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient.

Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient.

Combining, the above 2 cases still apply giving you an ambiguous answer.

Thus, E is the correct answer.

How do you get $$10^{2n} < 1$$ from $$10^{-n} > 10^n$$

$$10^{-n} > 10^n$$

Divide both sides by $$10^{-n}$$

$$1>10^n/10^{-n}$$ -->$$1>10^{2n}$$
_________________
Thanks,
Ramya
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

ramyanag wrote:
pclawong wrote:
Engr2012 wrote:
[quote="Bunuel"]If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Is (0.1)^n > (10)^n ---> $$10^{-n} > 10^n$$ ---> $$10^{2n} < 1$$ ---> $$10^{2n} < 10^0$$ ---> 2n < 0 ---> is n<0?

Per statement 1, n>-10, yes for n=-5 but no for n=5. Not sufficient.

Per statement 2, n<10, yes for n=-5 but no for n=5. Not sufficient.

Combining, the above 2 cases still apply giving you an ambiguous answer.

Thus, E is the correct answer.

How do you get $$10^{2n} < 1$$ from $$10^{-n} > 10^n$$

$$10^{-n} > 10^n$$

Divide both sides by $$10^{-n}$$

$$1>10^n/10^{-n}$$ -->$$1>10^{2n}$$[/quote]

Thank you so much! That's clear

Sent from my iPhone using GMAT Club Forum mobile app
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
Top Contributor
1
Bunuel wrote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Kudos for a correct solution.

Here's another approach:

Target question: Is (0.1)^n > (10)^n?
This is a good candidate for rephrasing the target question.

Since (0.1)^n is always POSITIVE, we can safely divide both sides of the inequality by (0.1)^n to get: 1 > [(10)^n]/[(0.1)^n]
There's a nice rule that says (a^n)/(b^n) = (a/b)^n
When we apply this rule to the right side of the inequality, we get: 1 > (10/0.1)^n
Simplify to get: Is 1 > 100^n?
Notice that, when n = 0, then 100^n = 100^0 = 1
So, when n > 0, then 100^n > 1, and when n < 0, then 100^n < 1
So, we can REPHRASE the target question as....
REPHRASED target question: Is n < 0?

Statement 1: n > -10
There are several values of n that satisfy statement 1. Here are two:
Case a: n = -9, in which case n < 0
Case b: n = 2, in which case n > 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n < 10
There are several values of n that satisfy statement 1. Here are two:
Case a: n = -9, in which case n < 0
Case b: n = 2, in which case n > 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

RELATED VIDEOS

_________________
Director  G
Joined: 02 Sep 2016
Posts: 649
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Bunuel can we play around with the statement in question like this?
I mean to say:

Its given that is 10^-n>10^n

So can we divide/subtract/multiple/add on both sides of an expression that is to be proved?

When should we not do it?

Thanks
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
Shiv2016 wrote:
Bunuel can we play around with the statement in question like this?
I mean to say:

Its given that is 10^-n>10^n

So can we divide/subtract/multiple/add on both sides of an expression that is to be proved?

When should we not do it?

Thanks

How to manipulate inequalities (adding, subtracting, squaring etc.).
_________________
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Bunuel chetan2u niks18 amanvermagmat

Quote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Why is it required for n to be an integer in Q stem?
How does one solve 1^0.5 or more specifically why does n
have to be an integer for 1^n to be 1?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Bunuel chetan2u niks18 amanvermagmat

Quote:
If n is an integer, is (0.1)^n greater than (10)^n?

(1) n > −10
(2) n < 10

Why is it required for n to be an integer in Q stem?
How does one solve 1^0.5 or more specifically why does n
have to be an integer for 1^n to be 1?

1^0.5=1^(1/2) which is square root of 1.
Mathematically it is possible to solve for non integer powers but then the question will become complicated and you might have to use calculator or log function.
Hence for simplicity it is mentioned that n is an integer. That’s my take on this question

Posted from my mobile device
Intern  B
Joined: 30 May 2017
Posts: 18
Location: India
Concentration: Finance, Strategy
Schools: Wharton, IESE, ISB, NUS
GPA: 4
WE: Engineering (Consulting)
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

Can we divide both sides by 10^(-n)( to simplify to question if n<0) if we dont know whether n is positive or negative in inequality. As we dont know what is n and hence the sign may flip. Please clear this doubt.
_________________
You say this is a problem , I say this must be an opportunity
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1178
Location: India
GPA: 3.82
If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

1
brains wrote:
Can we divide both sides by 10^(-n)( to simplify to question if n<0) if we dont know whether n is positive or negative in inequality. As we dont know what is n and hence the sign may flip. Please clear this doubt.

Hi brains

$$10^{-n}$$ will always be positive because a positive number that is 10 is being raised to some power. irrespective of the value of the power, the resulting number will always be positive

for e.g $$10^{-2}=\frac{1}{10^2}=0.01>0$$

similarly if $$10^2=100>0$$
Non-Human User Joined: 09 Sep 2013
Posts: 13276
Re: If n is an integer, is (0.1)^n greater than (10)^n?  [#permalink]

Show Tags

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.
_________________ Re: If n is an integer, is (0.1)^n greater than (10)^n?   [#permalink] 12 Sep 2019, 08:19
Display posts from previous: Sort by

If n is an integer, is (0.1)^n greater than (10)^n?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  