1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n What is n : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 19:39

### 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

# 1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n What is n

Author Message
Director
Joined: 14 Sep 2005
Posts: 993
Location: South Korea
Followers: 2

Kudos [?]: 156 [0], given: 0

1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n What is n [#permalink]

### Show Tags

28 Oct 2005, 05:30
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n

What is n?
_________________

Auge um Auge, Zahn um Zahn !

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 19

Kudos [?]: 293 [0], given: 0

Re: PS - Tricky calculation [#permalink]

### Show Tags

28 Oct 2005, 06:08
gamjatang wrote:
1/(n+1) < 1/31 + 1/32 + 1/33(=N) < 1/n

What is n?

we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10
Manager
Joined: 21 Sep 2005
Posts: 235
Followers: 2

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

Re: PS - Tricky calculation [#permalink]

### Show Tags

28 Oct 2005, 06:25
laxieqv wrote:
gamjatang wrote:
1/(n+1) < 1/31 + 1/32 + 1/33(=N) < 1/n

What is n?

we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10

Boy thats amazing!! I could never have thought of this solution.
SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 19

Kudos [?]: 293 [0], given: 0

Re: PS - Tricky calculation [#permalink]

### Show Tags

28 Oct 2005, 06:35
mohish wrote:
laxieqv wrote:
gamjatang wrote:
1/(n+1) < 1/31 + 1/32 + 1/33(=N) < 1/n

What is n?

we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10

Boy thats amazing!! I could never have thought of this solution.

hey, I'm a girl
Manager
Joined: 01 Aug 2005
Posts: 68
Followers: 1

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

### Show Tags

28 Oct 2005, 07:14
Hey laxie, care to guide us non experts through your reasoning? I am having a hard time following 1/(n+1) becoming 1/33 and also the second step where you have 3/33<N<3/31<3/30

"we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10"
SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 19

Kudos [?]: 293 [0], given: 0

### Show Tags

28 Oct 2005, 07:25
xennie wrote:
Hey laxie, care to guide us non experts through your reasoning? I am having a hard time following 1/(n+1) becoming 1/33 and also the second step where you have 3/33<N<3/31<3/30

"we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10"

I think this problem is well-manipulated ....I didn't solve it promtly, just looked around and wondered what if we compare 1/32 to 1/33 and 1/31 , luckily it came to solution.

we have 1/31>1/33 and 1/32>1/33 and 1/33=1/33
=> 1/31+1/32+1/33> 1/33+1/33+1/33= 3/33= 1/11=1/(n+1)
we have 1/31=1/31 and 1/32<1/31 and 1/33<1/31
=> 1/31+1/32+1/33< 1/31+1/31+1/31= 3/31 <3/30=1/10=1/n
------->n=10
Senior Manager
Joined: 05 Jan 2005
Posts: 254
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

31 Oct 2005, 18:26
Wow ! amazing solution from laxieqv.

SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 19

Kudos [?]: 293 [0], given: 0

### Show Tags

31 Oct 2005, 21:19
hkm_gmat wrote:

Let me type the question again first:
1/(n+1)< 1/31+1/32+1/33< 1/n

My reasonsing process is:
+Why don't we compare a sum of 3 numbers with a sum of 3 numbers instead of sth like the question?! -----> I try to express
1/(n+1) and 1/n as sums of three numbers:
1/(n+1) = 3/ [3(n+1)] = 1/(3n+3) + 1/(3n+3) + 1/(3n+3)
In the similar manner, we have 1/n = 1/(3n)+ 1/(3n)+ 1/(3n)
+since 3n+3 and 3n are very very close-----> I try to make the two ends of the inequality as close to ( 1/31+1/32+1/33) as possible -----> of coz, the best way is to make 3n+3= 30 and 3n= sth very close to 31( that is to say 30)---> i got n=10.

I don't know any website which teaches these techniques . As gamjatang told me that this question is 50-51 range, it's worth some reasoning
But from now on, you can hit similar questions like:
1/(n+1) < 1/41+1/42+1/43+1/44< 1/n
or 1/(n+1) < 1/51+1/52+1/53+1/54+1/55< 1/n
and so forth
Director
Joined: 21 Aug 2005
Posts: 793
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: PS - Tricky calculation [#permalink]

### Show Tags

31 Oct 2005, 21:51
laxieqv wrote:
gamjatang wrote:
1/(n+1) < 1/31 + 1/32 + 1/33(=N) < 1/n

What is n?

we have 1/33+1/33+1/33< 1/31+1/32+1/33< 1/31+1/31+1/31
---->3/33<N<3/31<3/30 -----> 1/11<N<1/10 ----> n=10

Laxie! You are way too smart for GMAT !
Current Student
Joined: 29 Jan 2005
Posts: 5238
Followers: 25

Kudos [?]: 378 [0], given: 0

### Show Tags

01 Nov 2005, 06:06
After staring at this problem for over 10 minutes, I have finally come to the following conclusion: GMAT doesn`t expect us to do the math here, it would take way too long! Obviously there is a logic trick involved which makes a Q50 problem seem like a Q35 problem.

1. Focus on the center: 1/31 + 1/32 + 1/33

This is slightly smaller than 3/31 <or> slightly larger than 3/33--->1/11

2. Now look at n: 1/(n+1)< 3/31 <or> 1/11 <1/n

3. Use 1/11 because THIS IS THE LOGIC TRICK TO THE PROBLEM.

4. 1/(n+1)=1/11 ----> n=10

5. Substitute back into the original equation

1/11<something between 1/11 and 3/31<1/10
SVP
Joined: 24 Sep 2005
Posts: 1890
Followers: 19

Kudos [?]: 293 [0], given: 0

### Show Tags

01 Nov 2005, 06:44
Bingo! You got it, Matt!!
01 Nov 2005, 06:44
Display posts from previous: Sort by