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# Set K consists of a finite number of consecutive odd

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Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Set K consists of a finite number of consecutive odd [#permalink]

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25 Oct 2009, 01:13
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Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.
[Reveal] Spoiler: OA
Manager
Joined: 08 Oct 2009
Posts: 70
Location: Denmark, Europe
Schools: Darden Class of 2012

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25 Oct 2009, 01:57
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.

(1) Insufficient. It could be (-37,-35), (-39,-37,-35,-33), etc.
(2) Insufficient. It could be any 8 (consecutive odd) numbers.

Combining information the set must be (-43,-41,-39,-37,-35,-33,-31,-29). The trick here is that they are consecutive odd numbers.

y-x is -29-(-43) = 14 and the answer is C.
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Joined: 02 Sep 2009
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25 Oct 2009, 14:12
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Expert's post
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.

From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

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Manager
Joined: 08 Oct 2009
Posts: 70
Location: Denmark, Europe
Schools: Darden Class of 2012

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25 Oct 2009, 15:23
D'oh!

I keep falling into these traps. Hopefully, practice will allow me to master them eventually...
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Joined: 09 Sep 2013
Posts: 16031
Re: Set K consists of a finite number of consecutive odd [#permalink]

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24 Jul 2014, 05:21
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Re: Set K consists of a finite number of consecutive odd [#permalink]

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22 Apr 2016, 18:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Set K consists of a finite number of consecutive odd [#permalink]

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30 Mar 2017, 15:22
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Joined: 02 Sep 2009
Posts: 39755
Re: Set K consists of a finite number of consecutive odd [#permalink]

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30 Mar 2017, 21:46
gardnej369 wrote:

There are 7 numbers in you set, not 8.
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Joined: 14 Nov 2016
Posts: 979
Location: Malaysia
Set K consists of a finite number of consecutive odd [#permalink]

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30 Mar 2017, 23:26
Bunuel wrote:
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.

From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

Source : Magoosh
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Math Expert
Joined: 02 Sep 2009
Posts: 39755
Re: Set K consists of a finite number of consecutive odd [#permalink]

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30 Mar 2017, 23:34
ziyuen wrote:
Bunuel wrote:
Economist wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =

(1) The average (arithmetic mean) of set K is –36.

(2) There are 8 numbers in set K.

From the stem: first term x, las t term y --> as we have consecutive odd integers then y=x+2(n-1), where n is the number of terms in the set. --> y-x=x+2(n-1)-x=2(n-1)

Basically we should find the number of terms to calculate y-x.

(1) The average=-36, --> (x+y)/2=-36 --> (2x+2(n-1))=-36 --> x+n-1=-36. Multiple choices for x and n. Not sufficient.

The mean of consecutive ODD integers is ODD, when # of terms is ODD.
The mean of consecutive ODD integers is EVEN, when # of terms is EVEN.
So, as -36 is even, that is why the mean =(first term+last term)/2=-36

(2) n=8. --> y-x=2(n-1)=14. Sufficient

Source : Magoosh

It's the formula of nth term of arithmetic progression. Check here: https://gmatclub.com/forum/math-sequenc ... 01891.html
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Re: Set K consists of a finite number of consecutive odd   [#permalink] 30 Mar 2017, 23:34
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