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 →

11 consecutive integers

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member
Thanked: 17 times
by rahul.s » Sun Jan 24, 2010 3:59 am
If eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of the eleven integers?

(1) The average of the first nine integers is 7.
(2) The average of the last nine integers is 9.

OA: D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Legendary Member
Posts: 1404
Joined: Tue May 20, 2008 6:55 pmFollowed by: 2 members
Thanked: 18 times

by tanviet » Sun Jan 24, 2010 5:55 am
the first number is x, second x+a, ....x+6a, so we have total first 9 is 9x+36a=7*9

we can infer total of 11x+(a+10a)*1/2*10

2, is similar
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members
Thanked: 653 times

by papgust » Sun Jan 24, 2010 7:14 am
11 consecutive numbers are listed from smallest to greatest. Mean of 11 numbers?

1. Avg of first nine integers is 7.

This means that 5th integer is 7. So 1st integer is 3. From here it is enough to know that mean could be calculated.
Sufficient.

2. Avg of last nine integers is 9.

This means that 7th integer is 9. So 1st integer is 3. Again sufficient.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 324
Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member
Thanked: 17 times

by rahul.s » Sun Jan 24, 2010 7:19 am
papgust wrote:11 consecutive numbers are listed from smallest to greatest. Mean of 11 numbers?

1. Avg of first nine integers is 7.

This means that 5th integer is 7. So 1st integer is 3. From here it is enough to know that mean could be calculated.
Sufficient.

2. Avg of last nine integers is 9.

This means that 7th integer is 9. So 1st integer is 3. Again sufficient.
thanks pagust :D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sat Jan 23, 2010 9:55 am
Thanked: 6 times

by VikingWarrior » Sun Jan 24, 2010 1:02 pm
11 consecutive numbers are listed from smallest to greatest. Mean of 11 numbers?

1. Avg of first nine integers is 7.

This means that 5th integer is 7. So 1st integer is 3. From here it is enough to know that mean could be calculated.
Sufficient.

2. Avg of last nine integers is 9.

This means that 7th integer is 9. So 1st integer is 3. Again sufficient.
I got the correct answer by the earlier method but I think I am missing a concept here. How do you know that the 5th integer is the mean of 1st five and 7th integer is mean of last nine. Please explain, Thanks :)
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 » Sun Jan 24, 2010 1:20 pm
VikingWarrior wrote:

I got the correct answer by the earlier method but I think I am missing a concept here. How do you know that the 5th integer is the mean of 1st five and 7th integer is mean of last nine. Please explain, Thanks :)
say the 10 integers are a, a+1, a+2, .... ,a+10

The mean of first 9 integers is(a+ a+1 + a+2.........+a+8)/9 = (9a+1+2+3+...+8)/9 = 9a+36/9 = a+4 (which indeed is the fifth integer)

The mean of last 9 integers is (a+2+ a+3 + a+4 + .....+ a+10) = (9a + 2+3+4....+10)/9= 9a+54/9 =a+6 (which is seventh integer in the list)
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
User avatar
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sat Jan 23, 2010 9:55 am
Thanked: 6 times

by VikingWarrior » Sun Jan 24, 2010 1:26 pm
Ajith, I know the method you have used. I used the same method and arrived at the answer but I was wondering if pagust used some theory to directly find out which no. was at which position by knowing the mean of consecutive nos.
Thanks for your explanation, appreciate the effort. :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Sun Jan 24, 2010 7:43 pm
VikingWarrior wrote:Ajith, I know the method you have used. I used the same method and arrived at the answer but I was wondering if pagust used some theory to directly find out which no. was at which position by knowing the mean of consecutive nos.
Thanks for your explanation, appreciate the effort. :)
When we have an odd number of terms in a set of consecutive numbers, the middle term is both the average (mean) and the median.

So, the average of the first 9 numbers (i.e. terms 1 through 9) will be the middle term in that subset, or the 5th term.

Similarly, the average of the last 9 numbers (i.e. terms 3 through 11) will be the middle term in that subset, or the 7th term.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 89
Joined: Sat Jan 23, 2010 9:55 am
Thanked: 6 times

by VikingWarrior » Sun Jan 24, 2010 11:47 pm
Thanks Stuart! Could anyone please give me a link to a good resource for this kind of theory (math) that is required/specific/important for GMAT? thanks :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1