It is currently 17 Nov 2017, 20:22

### 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 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

Director
Joined: 03 Sep 2006
Posts: 865

Kudos [?]: 1104 [2], given: 33

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

### Show Tags

26 Jan 2012, 07:32
2
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:27) correct 38% (01:33) wrong based on 266 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

Kudos [?]: 1104 [2], given: 33

Math Expert
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132522 [10], given: 12324

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

### Show Tags

26 Jan 2012, 09:31
10
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 #}:

$$\frac{3}{33}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}$$;

$$\frac{1}{11}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{3}{30}$$;

$$\frac{1}{10+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{1}{10}$$;

$$n=10$$.

_________________

Kudos [?]: 132522 [10], given: 12324

Manager
Joined: 07 May 2012
Posts: 74

Kudos [?]: 173 [2], given: 27

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

### Show Tags

27 May 2013, 06:23
2
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

Kudos [?]: 173 [2], given: 27

Manager
Joined: 07 May 2012
Posts: 74

Kudos [?]: 173 [0], given: 27

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

### Show Tags

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.

Kudos [?]: 173 [0], given: 27

Intern
Joined: 28 Feb 2013
Posts: 8

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

Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 740 Q48 V42
GPA: 3.45
WE: General Management (Non-Profit and Government)
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

### Show Tags

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)

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

Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 89

Kudos [?]: 200 [0], given: 23

Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

### Show Tags

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.

Kudos [?]: 200 [0], given: 23

Intern
Joined: 28 Dec 2012
Posts: 10

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

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

### Show Tags

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.

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

Senior Manager
Joined: 10 Jul 2013
Posts: 326

Kudos [?]: 425 [0], given: 102

### Show Tags

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 #} --> $$\frac{3}{33}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}$$ --> $$\frac{1}{11}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{3}{30}$$ --> $$\frac{1}{10+1}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}<\frac{3}{31}<\frac{1}{10}$$ --> $$n=10$$.

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

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

Asif vai.....

Kudos [?]: 425 [0], given: 102

Board of Directors
Joined: 17 Jul 2014
Posts: 2672

Kudos [?]: 431 [0], given: 200

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what [#permalink]

### Show Tags

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!

Kudos [?]: 431 [0], given: 200

Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what   [#permalink] 07 Oct 2016, 07:20
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

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