GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 06:16

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49495
If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

30 Jan 2014, 23:40
2
23
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:47) correct 37% (02:10) wrong based on 548 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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49495
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

30 Jan 2014, 23:40
4
2
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
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

31 Jan 2014, 00:35
4
1
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.

##### General Discussion
Manager
Joined: 20 Dec 2013
Posts: 244
Location: India
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

31 Jan 2014, 02:34
1
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: 49495
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

01 Feb 2014, 10:14
1
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
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: 545
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
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

Current Student
Joined: 12 Aug 2015
Posts: 2647
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

20 Dec 2016, 17:05
Great Official Question.
Here is what i did in this one =>

Given data =>
N consecutive odds
Mean =Median (For any evenly spaced set)=10
AS medan 10 => N must be even
Sum of deviations around the mean is always zero.
E.g => 9,11 OR 7,9,11,13

Hence we are adding elements in pair around the mean 10.
We need to get the least element now

Statement 1-->
Range =14
Series =>
3,5,7,9,11,13,15,17=> Least Integer will be 3
Hence Sufficient

Statement 2-->
Greasers integer =17

Number of terms tot he right of the median = Number of terms to the left of median
Median =10
11,13,15,17 => 4 terms to the right of it=> 4 terms must be there t the left of it.
Series => 3,5,7,9..
Hence least term =3
Hence Sufficient

Hence D

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 457
Location: India
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

23 Feb 2017, 04:53
PROMPT ANALYSIS
Let a, a+2, a+4, a+6…...n terms have average as 10
Sum of all values = na +n(n-1) = 10n or a +n-1 =10

SUPERSET
a can be any odd number.

TRANSLATION
In order to find a:
1# we need exact value of a
2# another equation with a and n as variable.

STATEMENT ANALYSIS

St 1: a +2n-2 - a =14 or n=8 therefore a =3 ANSWER. Option B, C, E eliminated.
St 2: a+2n-2 = 17.Solving with the equation in PROMPT, we get a =3 and n= 8. ANSWER. OptionA eliminated.

Option D.
_________________

GMAT Mentors

Non-Human User
Joined: 09 Sep 2013
Posts: 8177
Re: If the average (arithmetic mean) of n consecutive odd intege  [#permalink]

### Show Tags

08 May 2018, 01:08
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.
_________________
Re: If the average (arithmetic mean) of n consecutive odd intege &nbs [#permalink] 08 May 2018, 01:08
Display posts from previous: Sort by

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

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.