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 →

Algebra

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members
Location: International Space Station
Thanked: 11 times
by Aman verma » Wed Feb 24, 2010 6:57 am
Q: Consider the set S = { 2,3,4.............,2n + 1} ,where n is a positive integer greater than 2007.Define X as the average of odd integers in S and Y as the average of the even integers in S . What is the value of X - Y ?

a) 0

b)1

c)(1/2)n

d) (n+1)/2n

e)2008
800. Arjun's-Bird-Eye
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 184
Joined: Sat Apr 14, 2007 9:23 am
Location: Madison, WI
Thanked: 17 times

by ldoolitt » Wed Feb 24, 2010 7:26 am
Aman verma wrote:Q: Consider the set S = { 2,3,4.............,2n + 1} ,where n is a positive integer greater than 2007.Define X as the average of odd integers in S and Y as the average of the even integers in S . What is the value of X - Y ?

a) 0

b)1

c)(1/2)n

d) (n+1)/2n

e)2008
So I see a quick and slow way to do this.

Slow way (but more thorough)

Let K represent the number of terms in the set. Since 2n+1 is an odd number, and the set begins with an even number, there will be an equivalent number of odds and evens in the set. And thus each subset (odds and evens) has .5K numbers in it.

Average(odd) = sum of odds / .5 * K
Average(even) = sum of evens / .5*K

Average(odd-even) = sum of odds - sum of evens / .5K

But if you start writing out the sum of odds - sum of evens you have

-2+3-4+5-6+7+...

For each negative even there is an odd that is one more than it. You will have

1+1+1+...

How many 1's will you have? .5*K, since each sum to one takes 2 numbers (an odd and an even) and thus halves the number of terms in the set. The sum will be .5*K*1 = .5*K. Putting that back into the forumla you have:

.5*K / .5*K = 1

Or you could have simply notice that -2+3-4+5-6+7+... = 1+1+1+... and that the number of terms in each subset would be half the total number of terms in the set thus giving you an average of 1.
Last edited by ldoolitt on Wed Feb 24, 2010 7:27 am, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 40
Joined: Thu Mar 26, 2009 3:02 pm
Thanked: 3 times
GMAT Score:410

by Pedros » Wed Feb 24, 2010 7:27 am
I think the difference is 1 ( B )



Because ( 2n+1 ) is an odd number , I think about them as 2 different evenly spaced sets, the midpoint of the ODD set is only one space after that of the EVEN set . Regardless of the number of elements of each set the difference between the 2 midpoints will be 1.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 114
Joined: Mon Sep 22, 2008 3:51 am
Thanked: 8 times
GMAT Score:680

by Fiver » Wed Feb 24, 2010 9:32 am
Pedros wrote:I think the difference is 1 ( B )



Because ( 2n+1 ) is an odd number , I think about them as 2 different evenly spaced sets, the midpoint of the ODD set is only one space after that of the EVEN set . Regardless of the number of elements of each set the difference between the 2 midpoints will be 1.
Well done Pedros.

Though Pedros has developed a wonderful abstract solution to this problem, I thought i could give it an algebraic approach as well.

Both the sets of even and odd nos. are in AP.

Avg. of an AP = (FT + LT)/2
Avg. of the even set (X) = (2+2n)/2 = (1+n)
Avg. of the odd set (Y) = (3+2n+1)/2 = (2+n)

Y - X = 1
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members
Location: Arabian Sea
Thanked: 125 times

by ajith » Wed Feb 24, 2010 9:39 am
Aman verma wrote:Q: Consider the set S = { 2,3,4.............,2n + 1} ,where n is a positive integer greater than 2007.Define X as the average of odd integers in S and Y as the average of the even integers in S . What is the value of X - Y ?

a) 0

b)1

c)(1/2)n

d) (n+1)/2n

e)2008
There are 2n numbers down there

Sum of even numbers n/2(2+2n) = n(n+1)
Average of even numbers = n+1

Sum of odd numbers n/2(3+2n+1) = n(n+2)
Average of odd numbers = n+2

[spoiler]Difference = 1; B[/spoiler]
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 40
Joined: Thu Mar 26, 2009 3:02 pm
Thanked: 3 times
GMAT Score:410

by Pedros » Wed Feb 24, 2010 9:43 am
Fiver wrote:
Both the sets of even and odd nos. are in AP.

Avg. of an AP = (FT + LT)/2
Avg. of the even set (X) = (2+2n)/2 = (1+n)
Avg. of the odd set (Y) = (3+2n+1)/2 = (2+n)

Y - X = 1

As always FIVER......Impressive.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members
Location: International Space Station
Thanked: 11 times

by Aman verma » Thu Feb 25, 2010 2:06 am
Ans[spoiler]b)1[/spoiler].This was a sitter indeed and it was posted on purpose.There is one Expert who was constantly complaining that the questions posted are not real GMAT questions. Maybe he find this one easy and to his liking.The most realistic questions on GMAT can be found on the active GMAT question pool which ,I am afraid, nobody has access, atleast I don't have.
800. Arjun's-Bird-Eye
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1