Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

It is currently 23 Mar 2017, 17:11

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what

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

Hide Tags

2 KUDOS received
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 878
Followers: 6

Kudos [?]: 826 [2] , given: 33

GMAT ToolKit User
If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 26 Jan 2012, 07:32
2
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:28) correct 44% (01:32) wrong based on 277 sessions

HideShow timer Statistics

If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13
[Reveal] Spoiler: OA
Expert Post
10 KUDOS received
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37560
Followers: 7391

Kudos [?]: 99281 [10] , given: 11010

Re: n=? [#permalink]

Show Tags

New post 26 Jan 2012, 09:31
10
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13


Given: \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\).

Now, obviously \(3*(\frac{1}{33})<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<3*(\frac{1}{31})\), as {3 times the least #}<{given sum}<{3 times the largest #} --> \(\frac{3}{33}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}\) --> \(\frac{1}{11}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{3}{30}\) --> \(\frac{1}{10+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{1}{10}\) --> \(n=10\).

Answer: B.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Manager
Manager
User avatar
Joined: 07 May 2012
Posts: 75
Location: United States
Followers: 3

Kudos [?]: 145 [2] , given: 23

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 27 May 2013, 06:23
2
This post received
KUDOS
atalpanditgmat wrote:
gmacforjyoab wrote:
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13



Did it on similar grounds as Bunuel

1/(n+1) < ( 1/31 + 1/32 + 1/33) < 1/n
Substitute ( 1/31 + 1/32 + 1/33) to be 1/a
1/(n+1) < ( 1/a) < 1/n ......... ...................... hence n+1 > a > n--------------------------------- eq 1

1/a > 3/33 ( i.e 1/11) ... Hence a<11
from eq 1 --- n+1 >a>11 ................ n<a<11.. hence n <11

1/a < 3/31 ( or 1/10)..... hence a>10
from eq 1 --- n+1>a>10 .... hence n+1>10 ... n> 9

Ans n=10

hi gmacforjyoab,

I guess i am lacking some mathematics in the highlighted part. Could you please throw some light. It would be great help.

Regards
Atal Pandit


Since (1/n+1) < 1/a < 1/n , we can say that n+1 >a > n
( when u take the reciprocal of two numbers in an Inequality , the inequality flips )
Consider this ---- 1/4<1/3<1/2 , which would mean 4>3>2 ...

Oh and lets say - all the numbers were 1/33 , then the sum would be 3/33 , but all the numbers are not 1/33 , the other two numbers are 1/32 and 1/31 . and these two numbers are greater than 1/33 , hence the sum of 1/31 +1/32 + 1/33 would also be grater than 3/33
hence , 1/a > 3/33 i.e 1/11

HTH
Jyothi
_________________

Jyothi hosamani

1 KUDOS received
Intern
Intern
avatar
Joined: 25 Jul 2012
Posts: 12
Location: India
Concentration: Finance, Marketing
GMAT 1: 660 Q44 V37
Followers: 1

Kudos [?]: 10 [1] , given: 2

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 25 May 2013, 09:36
1
This post received
KUDOS
gmacforjyoab wrote:
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13



Did it on similar grounds as Bunuel

1/(n+1) < ( 1/31 + 1/32 + 1/33) < 1/n ...................... hence n+1 > a > n--------------------------------- eq 1
Substitute ( 1/31 + 1/32 + 1/33) to be 1/a
1/(n+1) < ( 1/a) < 1/n
1/a > 3/33 ( i.e 1/11) ... Hence a<11
from eq 1 --- n+1 >a>11 ................ n<a<11.. hence n <11

1/a < 3/31 ( or 1/10)..... hence a>10
from eq 1 --- n+1>a>10 .... hence n+1>10 ... n> 9

Ans n=10



I did it on the same grounds..

Answers is coming out to be 10.
_________________

If you like my post, consider giving me KUDOS :-)

Expert Post
Math Expert
User avatar
G
Joined: 02 Sep 2009
Posts: 37560
Followers: 7391

Kudos [?]: 99281 [0], given: 11010

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 24 May 2013, 04:42
Manager
Manager
User avatar
Joined: 07 May 2012
Posts: 75
Location: United States
Followers: 3

Kudos [?]: 145 [0], given: 23

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 25 May 2013, 09:13
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13



Did it on similar grounds as Bunuel

1/(n+1) < ( 1/31 + 1/32 + 1/33) < 1/n
Substitute ( 1/31 + 1/32 + 1/33) to be 1/a
1/(n+1) < ( 1/a) < 1/n ......... ...................... hence n+1 > a > n--------------------------------- eq 1

1/a > 3/33 ( i.e 1/11) ... Hence a<11
from eq 1 --- n+1 >a>11 ................ n<a<11.. hence n <11

1/a < 3/31 ( or 1/10)..... hence a>10
from eq 1 --- n+1>a>10 .... hence n+1>10 ... n> 9

Ans n=10
_________________

Jyothi hosamani


Last edited by gmacforjyoab on 26 May 2013, 11:54, edited 1 time in total.
Intern
Intern
avatar
Joined: 28 Feb 2013
Posts: 8
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 740 Q48 V42
GPA: 3.45
WE: General Management (Non-Profit and Government)
Followers: 0

Kudos [?]: 8 [0], given: 0

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 26 May 2013, 05:25
Approximate 1/31 + 1/32 + 1/33 = 0.09+

Now POE. B fits the inequality.

0.09 (1/11) < 0.09+ < 0.1 (1/10)
Manager
Manager
avatar
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 90
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Followers: 0

Kudos [?]: 159 [0], given: 23

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 27 May 2013, 02:36
gmacforjyoab wrote:
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13



Did it on similar grounds as Bunuel

1/(n+1) < ( 1/31 + 1/32 + 1/33) < 1/n
Substitute ( 1/31 + 1/32 + 1/33) to be 1/a
1/(n+1) < ( 1/a) < 1/n ......... ...................... hence n+1 > a > n--------------------------------- eq 1

1/a > 3/33 ( i.e 1/11) ... Hence a<11
from eq 1 --- n+1 >a>11 ................ n<a<11.. hence n <11

1/a < 3/31 ( or 1/10)..... hence a>10
from eq 1 --- n+1>a>10 .... hence n+1>10 ... n> 9

Ans n=10

hi gmacforjyoab,

I guess i am lacking some mathematics in the highlighted part. Could you please throw some light. It would be great help.

Regards
Atal Pandit
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

Intern
Intern
avatar
Joined: 28 Dec 2012
Posts: 10
Followers: 0

Kudos [?]: 22 [0], given: 19

GMAT ToolKit User
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 08 Aug 2013, 10:27
1/n> 1/31+1/32+1/33> 1/33+ 1/33 + 1/33 = 3/33 = 1/11 ====> n<11

1/(n+1)< 1/31 + 1/32+ 1/33 < 1/31 + 1/31 + 1/31 = 3/31 ====> n>9,3

Then, n=10.

B.
Senior Manager
Senior Manager
avatar
Joined: 10 Jul 2013
Posts: 335
Followers: 3

Kudos [?]: 336 [0], given: 102

Re: n=? [#permalink]

Show Tags

New post 09 Aug 2013, 05:11
Bunuel wrote:
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13


Given: \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\).

Now, obviously \(3*(\frac{1}{33})<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<3*(\frac{1}{31})\), as {3 times the least #}<{given sum}<{3 times the largest #} --> \(\frac{3}{33}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}\) --> \(\frac{1}{11}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{3}{30}\) --> \(\frac{1}{10+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{1}{10}\) --> \(n=10\).

Answer: B.

...............

Amazing solution..... glad to learn this.....
_________________

Asif vai.....

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 14375
Followers: 602

Kudos [?]: 174 [0], given: 0

Premium Member
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 23 Jan 2015, 03:00
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 14375
Followers: 602

Kudos [?]: 174 [0], given: 0

Premium Member
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 30 Mar 2016, 06:22
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

SVP
SVP
User avatar
S
Joined: 17 Jul 2014
Posts: 2375
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (D)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 25

Kudos [?]: 291 [0], given: 147

GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 07 Oct 2016, 07:20
solved it the other way...and probably the fastest way...
suppose we have 1/33 + 1/33 + 1/33
we have 3/33 or 1/11
since we have 1/31 and 1/32, logically, the result would be slightly more than 1/11.
10 works just fine...
we have 1/n+1 => 1/11, and we have 1/10

10 works just fine!
Manager
Manager
avatar
Joined: 29 Aug 2008
Posts: 114
Followers: 2

Kudos [?]: 38 [0], given: 284

If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

Show Tags

New post 17 Oct 2016, 02:57
gmacforjyoab wrote:
LM wrote:
If n is an integer and \(\frac{1}{n+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{1}{n}\), then what is the value of n?

A) 9
B) 10
C) 11
D) 12
E) 13



Did it on similar grounds as Bunuel

1/(n+1) < ( 1/31 + 1/32 + 1/33) < 1/n
Substitute ( 1/31 + 1/32 + 1/33) to be 1/a
1/(n+1) < ( 1/a) < 1/n ......... ...................... hence n+1 > a > n--------------------------------- eq 1

1/a > 3/33 ( i.e 1/11) ... Hence a<11
from eq 1 --- n+1 >a>11 ................ n<a<11.. hence n <11

1/a < 3/31 ( or 1/10)..... hence a>10
from eq 1 --- n+1>a>10 .... hence n+1>10 ... n> 9

Ans n=10


Can someone pls explain the highlighted part.

TIA
If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what   [#permalink] 17 Oct 2016, 02:57
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic For the sequence a1, a2, a3 ... an, an is defined by a_n=1/n−1/(n+1) Bunuel 2 20 Feb 2017, 02:01
2 Experts publish their posts in the topic What is the smallest positive integer n for which n!/9^9 is an integer Bunuel 6 16 Feb 2017, 03:35
In N is a positive integer and 14N/60 is an integer. What is the small stonecold 1 23 Aug 2016, 10:26
7 Experts publish their posts in the topic If p and n are positive integers, with p > n, what is the average of n Bunuel 5 14 Sep 2015, 22:53
1 The sequence x1, x2, x3,..., is such that Xn = 1/n - 1/(n+1) aeros232 2 22 Sep 2012, 10:19
Display posts from previous: Sort by

If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what

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


GMAT Club MBA Forum Home| About| 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®.