• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Consecutiveness of n

This topic has 8 expert replies and 8 member replies
Goto page
  • 1,
  • 2
Next

Consecutiveness of n

Post
Hi! This was from one of the MGMAT CATs. Can some one please explain?

A list contains n distinct integers. Are all n integers consecutive?

(1) The average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed.

(2) The positive difference between any two numbers in the list is always less than n.

OA is D

  • +1 Upvote Post
  • Quote
  • Flag
Legendary Member
Joined
14 Aug 2012
Posted:
1556 messages
Followed by:
34 members
Upvotes:
448
Target GMAT Score:
750
GMAT Score:
650
Post
N = A, B,C,D,E,F

Statement 1:
(B+C+D+E+F)/5 = 1 + (A+B+C+D+E)/5
B+C+D+E+F = 5 + A+B+C+D+E
F-A = 5
Only consecutive number series is possible to give such a result
Hence, consecutive.
SUFFICIENT

Statement 2:
F-A < 6
Since, numbers are different..
Only consecutive number series is possible to give such a result
SUFFICIENT

Answer {D}

_________________
R A H U L

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
^^ The post above shows that the statements are sufficient for n = 6, but they don't necessarily represent all values of n. (There's no reason to assume that n is 6.)

If you're going to take the "plug in numbers" approach, then, good -- it's an effective approach -- but you should definitely try more than one value of n!

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Legendary Member
Joined
14 Aug 2012
Posted:
1556 messages
Followed by:
34 members
Upvotes:
448
Target GMAT Score:
750
GMAT Score:
650
Post
lunarpower wrote:
^^ The post above shows that the statements are sufficient for n = 6, but they don't necessarily represent all values of n. (There's no reason to assume that n is 6.)

If you're going to take the "plug in numbers" approach, then, good -- it's an effective approach -- but you should definitely try more than one value of n!
Ron, from the result of statement one

F-A = 5 [A,B,C,D,E & F are integer values]

it's pretty much clear that RHS would always be one less than the value of "n" I could think of..

Hence, trying multiple values of "n" would be merely waste of time that I could have saved for next questions..That's why i din't try more values. Smile ..

_________________
R A H U L

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
theCodeToGMAT wrote:
Ron, from the result of statement one

F-A = 5 [A,B,C,D,E & F are integer values]

it's pretty much clear that RHS would always be one less than the value of "n" I could think of..

Hence, trying multiple values of "n" would be merely waste of time that I could have saved for next questions..That's why i din't try more values. :) ..
Fair enough. If you see the seeds of a strong pattern, then, great. Nicely done.

I guess my point is that, since you're going to the trouble of posting these things on a public forum, you may as well lay out that part of the reasoning more explicitly.
E.g., "I can tell that the same thing will happen for other n's." Or something like that.

In other words, even if your solution is awesome, there's little point in posting it without that kind of explanatory detail.
(Maybe I misunderstand the point of view of people on the forum, though. For instance, there are tons and tons of posts on every thread that say things like "I choose B", with no explanation whatsoever. Such posts add zero value to the discussion -- and are frustrating to scroll through, if there are lots of them -- but people still post them.)

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Legendary Member
Joined
14 Aug 2012
Posted:
1556 messages
Followed by:
34 members
Upvotes:
448
Target GMAT Score:
750
GMAT Score:
650
Post
Thanks Ron. Yeah, I agree with you .. I will try my best to post "Sound" solutions Smile

_________________
R A H U L

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts
Joined
01 Jun 2012
Posted:
89 messages
Followed by:
2 members
Upvotes:
6
Post
Hi Ron and theCodeToGMAT,

I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum.

I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again?

Again, apologies for missing this thread.

Thanks

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
sidceg wrote:
Hi Ron and theCodeToGMAT,

I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum.

I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again?

Again, apologies for missing this thread.

Thanks
"Positive difference" is exactly what it says. It's the difference between two numbers, expressed as a positive number.
E.g., the positive difference between 3 and 7 is 4. The positive difference between 7 and 3 is also 4.

For statement 2, the only thing you really need to think about is the difference between the biggest and smallest values in the set. (If you don't see why that is so, think about it for a bit.)
Try making any set, at all, that doesn't consist entirely of consecutive integers. See whether you can get that difference to be less than N.

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Senior | Next Rank: 100 Posts
Joined
01 Jun 2012
Posted:
89 messages
Followed by:
2 members
Upvotes:
6
Post
lunarpower wrote:
sidceg wrote:
Hi Ron and theCodeToGMAT,

I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum.

I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again?

Again, apologies for missing this thread.

Thanks
"Positive difference" is exactly what it says. It's the difference between two numbers, expressed as a positive number.
E.g., the positive difference between 3 and 7 is 4. The positive difference between 7 and 3 is also 4.

For statement 2, the only thing you really need to think about is the difference between the biggest and smallest values in the set. (If you don't see why that is so, think about it for a bit.)
Try making any set, at all, that doesn't consist entirely of consecutive integers. See whether you can get that difference to be less than N.
I tried the following cases.

1,2,3: 3-2<3 --> Yes
4,5,6,7: 7-4<4 --> Yes
-3,-2,-1,0,1: 1-(-3)<5 --> Yes

But what about [-5,0,5,10]? Are these integers consecutive?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
"Consecutive" means "next to each other in sequence, without skipping anything".
The difference between any two consecutive integers is 1.

5, 10, 15, 20, ... would be consecutive multiples of 5. But they're not consecutive integers, since there are other integers between them.

--

More importantly, those values are irrelevant to the problem at hand, because they don't satisfy statement 2.

Statement 2 says that the difference between any 2 integers in the set is LESS than N.
Try getting that to happen with anything other than a set of consecutive integers. Not gonna happen.

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Senior | Next Rank: 100 Posts
Joined
01 Jun 2012
Posted:
89 messages
Followed by:
2 members
Upvotes:
6
Post
lunarpower wrote:
"Consecutive" means "next to each other in sequence, without skipping anything".
The difference between any two consecutive integers is 1.

5, 10, 15, 20, ... would be consecutive multiples of 5. But they're not consecutive integers, since there are other integers between them.
Okay I often got confused between the consecutive numbers as numbers spaced equally.

lunarpower wrote:
More importantly, those values are irrelevant to the problem at hand, because they don't satisfy statement 2.

Statement 2 says that the difference between any 2 integers in the set is LESS than N.
Try getting that to happen with anything other than a set of consecutive integers. Not gonna happen.
Since I had considered consecutive numbers as numbers equally spaced, I tried the above numbers also which yielded a NO. So with all other cases YES and this one case NO, I concluded that statement II is not sufficient.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
Ah, I see. But, no, that's not what "consecutive integers" means.

There's a different name for that sort of thing -- I think it's "arithmetic progression" or "arithmetic sequence", or something like that -- but you won't need to know that name for the gmat exam.

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
Senior | Next Rank: 100 Posts
Joined
01 Jun 2012
Posted:
89 messages
Followed by:
2 members
Upvotes:
6
Post
Alright! Thanks Ron Smile

  • +1 Upvote Post
  • Quote
  • Flag
Newbie | Next Rank: 10 Posts Default Avatar
Joined
04 Jan 2014
Posted:
7 messages
Post
sidceg wrote:
Hi! This was from one of the MGMAT CATs. Can some one please explain?

A list contains n distinct integers. Are all n integers consecutive?

(1) The average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed.

(2) The positive difference between any two numbers in the list is always less than n.

OA is D
Statement I is sufficient

Let us say n = 4 and the numbers are 4, 5, 6 and 7

If we remove 4 then the average is 6
If we remove 7 then the average is 5 which satisfies with the statement

Now lets go algebra:

If the numbers are {x, x+1, x+2.....x+n-1} with average (2x + n - 1)/2 (First + last)/2

If we remove x then the average will become (x + 1 + x + n - 1)/2 = (2x + n)/2 increasing by 1/2
If we remove x + n - 1 the average will become (x + x + n -2)/2 = (2x + n -2)/2 decreasing by 1/2

Hence the difference will always be the 1 between them.

Statement II is sufficient:

If the numbers are {x, x+1, x+2.....x+n-1}

If we subtract the first and the last we will get = |x + n - 1 - x| = n - 1 which is always less than n. Now is there any other set which can have that. Since the members of the set are distinct it is not possible to have that.

Answer is D.

_________________
Perfect Scores

If you think our post was valuable then please encourage us with Kudos Smile

To learn GMAT for free visit:

https://Perfect-Scores.com
https://Youtube.com/PerfectScores
https://Facebook.com/PerfectScores

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor
Joined
03 Mar 2008
Posted:
3380 messages
Followed by:
1498 members
Upvotes:
2256
GMAT Score:
800
Post
PerfectScores wrote:
Statement I is sufficient

Let us say n = 4 and the numbers are 4, 5, 6 and 7

If we remove 4 then the average is 6
If we remove 7 then the average is 5 which satisfies with the statement

Now lets go algebra:

If the numbers are {x, x+1, x+2.....x+n-1} with average (2x + n - 1)/2 (First + last)/2

If we remove x then the average will become (x + 1 + x + n - 1)/2 = (2x + n)/2 increasing by 1/2
If we remove x + n - 1 the average will become (x + x + n -2)/2 = (2x + n -2)/2 decreasing by 1/2

Hence the difference will always be the 1 between them.
^^ It appears here that you're starting with a set of consecutive integers, and trying to prove statement 1. That's not the way it works, although you'll get lucky with the answer here.

If you want to take an approach like this one, then you must also prove that starting with any other set (i.e., a set that doesn't consist entirely of consecutive integers) won't give a difference of 1.

_________________
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

  • +1 Upvote Post
  • Quote
  • Flag
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Top First Responders*

1 GMATGuruNY 56 first replies
2 Brent@GMATPrepNow 51 first replies
3 Jay@ManhattanReview 49 first replies
4 fskilnik@GMATH 46 first replies
5 Rich.C@EMPOWERgma... 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

180 posts
2 image description fskilnik@GMATH

GMATH Teacher

162 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

94 posts
4 image description Max@Math Revolution

Math Revolution

91 posts
5 image description GMATGuruNY

The Princeton Review Teacher

78 posts
See More Top Beat The GMAT Experts