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

 It is currently 16 Oct 2018, 09:34

### 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

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 803
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
4
13
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:52) correct 36% (02:22) wrong based on 339 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
Math Expert
Joined: 02 Sep 2009
Posts: 49915
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
8
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 #}:

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

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

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

$$n=10$$.

_________________
##### General Discussion
Manager
Joined: 07 May 2012
Posts: 64
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

Updated on: 26 May 2013, 11:54
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

Originally posted by gmacforjyoab on 25 May 2013, 09:13.
Last edited by gmacforjyoab on 26 May 2013, 11:54, edited 1 time in total.
Intern
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)
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)
Manager
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 86
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.

Manager
Joined: 07 May 2012
Posts: 64
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
1
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

Intern
Joined: 28 Dec 2012
Posts: 9
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
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
Joined: 10 Jul 2013
Posts: 315

### 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.....

Board of Directors
Joined: 17 Jul 2014
Posts: 2654
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!
Non-Human User
Joined: 09 Sep 2013
Posts: 8415
Re: If n is an integer and 1/(n+1)<1/31+1/32+1/33<1/n, then what  [#permalink]

### Show Tags

23 Apr 2018, 14:25
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 and 1/(n+1)<1/31+1/32+1/33<1/n, then what &nbs [#permalink] 23 Apr 2018, 14:25
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

 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®.