BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Value of n??

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 15, 2010 10:41 am
apoorva.srivastva wrote:If 1/(n+1)<1/31+1/32+1/33<1/n, n=?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
please solve it algebraically!!
I don't believe an algebraic solution is the way to go here.
First, recognize that 1/33 < 1/32 (and 1/33 < 1/31)
So, we know that 1/33 + 1/33 + 1/33 < 1/31 + 1/32 + 1/33
We should also see that 1/33 and 1/32 are very close in value so we might say that (1/33 + 1/33 + 1/33) is just a little bit less than (1/31 + 1/32 + 1/33)

Also recognize that 1/33 + 1/33 + 1/33 = 1/11
So 1/33 + 1/33 + 1/33 < 1/31 + 1/32 + 1/33 can be rewritten as 1/11 < 1/31 + 1/32 + 1/33

Compare this to the inequality in our question: 1/(n+1)<1/31+1/32+1/33
We can see that n+1 = 11, which means n=10
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 146
Joined: Wed Aug 27, 2008 5:41 am
Thanked: 3 times

by apoorva.srivastva » Fri Jan 15, 2010 10:56 am
wowwieeee...great approach!!
thanks brent!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Sun Oct 11, 2009 10:15 am

by zonda12 » Fri Jan 15, 2010 9:52 pm
Just a little concern: how in the hell is an average person supposed to come up with that approach in under minutes? I mean, my math is decent, but no way near the level of thinking of that on the spot. I don't wish to belittle your answer, because you are indeed a genuius; I'm merely curious.

Is this a normal (easy/mid) question for gmat, or is this considered at a hard one (750+ score) one?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 15, 2010 10:53 pm
zonda12 wrote:Just a little concern: how in the hell is an average person supposed to come up with that approach in under minutes? I mean, my math is decent, but no way near the level of thinking of that on the spot. I don't wish to belittle your answer, because you are indeed a genuius; I'm merely curious.

Is this a normal (easy/mid) question for gmat, or is this considered at a hard one (750+ score) one?
That's a valid point. Sometimes when explaining a solution to a problem it's easy to make it sound like one just steps up and . . . voila . . . everything just falls into place. The actual process is much more complex, and seldom so straightforward.

Here's another way to tackle the question:
First, I'd love to know the sum of 1/31 + 1/32 + 1/33 without actually doing all of the calculations.
One option would be to conclude that, since 1/32 falls between the other two fractions, then 1/31 + 1/32 + 1/33 should be approximately equal to 1/32 + 1/32 + 1/32 = 3/32

At this point I ask how 3/32 compares with 1/n and 1/(n+1)

I know that 3/32 is a little less than 1/10 since 3.2/32 would be equal to 1/10
I also know that 3/32 is greater than 1/11 since 3/33 = 1/11
So, from here, I could conclude that 1/11 < 1/31 + 1/32 + 1/33 < 1/10

The original question features the inequality 1/(n+1) < 1/31 + 1/32 + 1/33 < 1/n
So, we can see that 1/11 = 1/(n+1) . . . which means n=10

I'm finding it hard to predict the degree of difficulty on this one. I'm going to go out on a limb and say it falls somewhere around 650 (even though I should be predicting an approximate raw score :-))
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1