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

 It is currently 24 Jul 2016, 11:41

### 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

Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76328 [1] , given: 9973

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

### Show Tags

30 Jan 2014, 23:40
1
KUDOS
Expert's post
11
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:28) correct 39% (01:53) wrong based on 332 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 66
Category: Arithmetic Statistics
Page: 157
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76328 [3] , given: 9973

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

### Show Tags

30 Jan 2014, 23:40
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
SOLUTION

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.

_________________
Manager
Joined: 23 Jun 2008
Posts: 85
Location: Australia
Schools: AGSM '22
GMAT Date: 04-01-2014
Followers: 1

Kudos [?]: 40 [4] , given: 24

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

### Show Tags

31 Jan 2014, 00:35
4
KUDOS
What we know:
If n consecutive integers have arithmetic mean of 10; those numbers are distributed either side of 10 perfectly symmetrically.

Statement (1)

Range is the difference between the greatest and the least numbers in the series.
If the range is known the least of these integers must be less than the mean, i.e. 10 - (14/2) = 3 (Note we don't really need to calculate this... to know we can is sufficient.)

Statement (2)

Similarly, the distance from the greatest number to mean equals to the distance from mean to the least number. So knowing the greatest number also sufficient to calculate the least number. (in this case 10 - (17 - 10) = 3)

The answer is D : Both Statement 1 and Statement 2 are sufficient ALONE .

Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 66
Category: Arithmetic Statistics
Page: 157
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________

Kudos (+1) if you find this post helpful.

Senior Manager
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 76 [0], given: 29

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

### Show Tags

31 Jan 2014, 02:34
1
This post was
BOOKMARKED
Ans. D
Let the series start from x=>x,(x+2),(x+4),...(x+k) id the series.
Average=[x+(x+k)]/2=10(1)
x+(x+k)=20=>2x+k=20

Given in S1, x+k-x=14=>k=14.We can find out x,the smallest integer.Sufficient

From S2: x+k=17
By putting this value in (1),we can get x,the answer.
Sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76328 [0], given: 9973

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

### Show Tags

01 Feb 2014, 10:14
Expert's post
SOLUTION

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.

_________________
Intern
Joined: 24 Jul 2014
Posts: 1
Followers: 0

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

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

### Show Tags

15 Aug 2014, 08:52
I did it this way.

Since consecutive odd integers are evenly spaced then avg = median = 10

Since median is even (10) for a set of consecutive odd integers, set must have even number of integers
Ex: if set has 3,5,7 then median 5 (odd)
if set has 3,5,7,9 then median = 5+7/2 = 6 (even)

so we can say (x+ (x+2))/2 = 10 => 2x+2=20 => x=9.
So middle terms of the set are 9 & 11. If I know one more thing like range or first/last term I can create full list.

Hence both statements are sufficient. Ans: D
Director
Joined: 10 Mar 2013
Posts: 605
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 169 [0], given: 200

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

### Show Tags

13 Jun 2015, 05:47
(Min + Max)/2 = 10 --> Min + Max=20
1)Range means Max - Min=14, sow we have two equations and two unknowns --> can be solved Min = 3
2)Max=17, Plug it here Min+Max=20 --> Min=3
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Re: If the average (arithmetic mean) of n consecutive odd intege   [#permalink] 13 Jun 2015, 05:47
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
49 If the average (arithmetic mean) of n consecutive odd 15 09 Dec 2010, 15:43
17 If the average (arithmetic mean) of n consecutive odd intege 5 26 Nov 2009, 12:12
Display posts from previous: Sort by