Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Jul 2016, 10:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the average (arithmetic mean) of n consecutive odd intege

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Nov 2009
Posts: 14
Followers: 1

Kudos [?]: 50 [0], given: 0

If the average (arithmetic mean) of n consecutive odd intege [#permalink]

### Show Tags

26 Nov 2009, 12:12
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:16) correct 31% (01:16) wrong based on 105 sessions

### HideShow timer Statistics

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14
(2) The greatest of the n integers is 17
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Dec 2012, 08:16, edited 1 time in total.
Edited the question and added the OA.
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 251 [0], given: 31

Re: Quant Guide DS 66 [#permalink]

### Show Tags

26 Nov 2009, 14:13
JimmyWorld wrote:
Hi,

I am unsure about the explanation on DS #66 of Quant Guide.

Can someone explain the answer to 2) for me?

If the average(arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers.

1) The range of n integers is 14.
2) The greatest of the n integers is 17.

I understood 1) but didnt know how to get 2).

n is a set of consecutive odd integers and the last one being 17

17 + 15 = 22/2 = 11
17 + 15 + 13 = 45/3 = 15
working backwards you'll find 3 is the smallest number, 8 numbers total 80 and the average 10
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 251 [1] , given: 31

Re: Quant Guide DS 66 [#permalink]

### Show Tags

26 Nov 2009, 15:00
1
KUDOS
JimmyWorld wrote:
Thanks for the response. I was just wondering what would be a faster way to do this problem. If I were to work backwards to find when the average is 10, it would take me longer then 2 minutes to do that. Is there a quick way to figure out that the least number would be 3?

in a group of consecutive integers the average is also the median
10 would be the median
17 the largest

that would have to make 3 the smallest
Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 52 [0], given: 562

Re: If the average(arithmetic mean) of n consecutive odd integer [#permalink]

### Show Tags

16 Dec 2012, 00:05
Bunuel,
how to solve this using algebraic approach?

Regards,
Sach
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Manager
Joined: 27 Feb 2012
Posts: 137
Followers: 1

Kudos [?]: 44 [1] , given: 22

Re: If the average(arithmetic mean) of n consecutive odd integer [#permalink]

### Show Tags

16 Dec 2012, 00:44
1
KUDOS
Sachin9 wrote:
Bunuel,
how to solve this using algebraic approach?

Regards,
Sach

Let me give it a try.

Say the first term of the progression, i.e. the least of the integers is a. Hence n-th term of the progression, i.e. the largest of the integers will be [a + 2(n - 1)].

Therefore, Range = Max - Min = [a + 2(n - 1)] - a = 2(n - 1)
and, Arithmetic Mean = (Max + Min)/2 = [a + 2(n - 1) + a]/2 = [a + (n - 1)]

Now, [a + (n - 1)] = 10 => (a + n) = 11

Thus, we can determine the value of a, once we know the value of n.

Statement 1: Range = 14
Hence, 2(n - 1) = 14
=> n = 8 => We can determine the value of a.

Sufficient

Statement 2: [a + 2(n - 1)] = 17
We have two equations in two unknowns. Hence, we can determine the value of a.
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 34106
Followers: 6099

Kudos [?]: 76746 [12] , given: 9981

Re: If the average(arithmetic mean) of n consecutive odd integer [#permalink]

### Show Tags

16 Dec 2012, 08:18
12
KUDOS
Expert's post
1
This post was
BOOKMARKED
Sachin9 wrote:
Bunuel,
how to solve this using algebraic approach?

Regards,
Sach

If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean equals to the average of the first and the last terms, so in our case $$mean=10=\frac{x_1+x_{n}}{2}$$ --> $$x_1+x_{n}=20$$. Question: $$x_1=?$$

(1) The range of the n integers is 14 --> the range of a set is the difference between the largest and smallest elements of a set, so $$x_{n}-x_1=14$$ --> solving for $$x_1$$ --> $$x_1=3$$. Sufficient.

(2) The greatest of the n integers is 17 --> $$x_n=17$$ --> $$x_1+17=20$$ --> $$x_1=3$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-average-arithmetic-mean-of-n-consecutive-odd-106036.html
_________________
Re: If the average(arithmetic mean) of n consecutive odd integer   [#permalink] 16 Dec 2012, 08:18
Similar topics Replies Last post
Similar
Topics:
What is the average (arithmetic mean) of fifteen consecutive integers? 2 26 May 2016, 11:39
10 If the arithmetic mean of n consecutive odd integers is 20, what is 8 19 Aug 2015, 03:05
1 If m is a positive odd integer, what is the average (arithmetic mean) 2 28 Jul 2015, 07:33
19 If the average (arithmetic mean) of n consecutive odd intege 6 30 Jan 2014, 23:40
49 If the average (arithmetic mean) of n consecutive odd 15 09 Dec 2010, 15:43
Display posts from previous: Sort by