It is currently 12 Dec 2017, 21:28

### 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

Author Message
TAGS:

### Hide Tags

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 127

Kudos [?]: 489 [5], given: 210

Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
If the average (arithmetic mean) of n consecutive odd [#permalink]

### Show Tags

09 Dec 2010, 14:43
5
KUDOS
21
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:18) correct 38% (01:24) wrong based on 676 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

Kudos [?]: 489 [5], given: 210

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135410 [27], given: 12692

Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]

### Show Tags

09 Dec 2010, 14:59
27
KUDOS
Expert's post
12
This post was
BOOKMARKED
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

_________________

Kudos [?]: 135410 [27], given: 12692

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7791

Kudos [?]: 18108 [9], given: 236

Location: Pune, India
Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]

### Show Tags

12 Dec 2010, 04:24
9
KUDOS
Expert's post
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

If mean of consecutive odd integers is 10, the sequence of numbers will be something like this:
9, 11 or
7, 9, 11, 13 or
5, 7, 9, 11, 13, 15 or
3, 5, 7, 9, 11, 13, 15, 17 or
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
etc
Every time you add a number to the left, you need to add one to the right to keep the mean 10. The smallest sequence will have 2 numbers 9 and 11, the largest will have infinite numbers.

Stmnt 1: Only one possible sequence: 3, 5, 7, 9, 11, 13, 15, 17 will have range 14. Least of the integers is 3. Sufficient.
Stmnt 2: Only one possible sequence:3, 5, 7, 9, 11, 13, 15, 17
Least of the integers is 3. Sufficient.

Note: You don't actually have to do all this. All such sequences will have distinct number of elements, greatest number, smallest number and range. So each statement alone will be sufficient.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18108 [9], given: 236 TOEFL Forum Moderator Joined: 16 Nov 2010 Posts: 1586 Kudos [?]: 607 [2], given: 40 Location: United States (IN) Concentration: Strategy, Technology Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink] ### Show Tags 06 Apr 2011, 07:28 2 This post received KUDOS (1) so (a + a + 14)/2 = 10 => 2a = 20 - 14 = 6 => a =3 (2) (a+17)/2 = 10 => a = 3 Answer - D (a+17) _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Kudos [?]: 607 [2], given: 40 Senior Manager Status: Bring the Rain Joined: 17 Aug 2010 Posts: 389 Kudos [?]: 47 [1], given: 46 Location: United States (MD) Concentration: Strategy, Marketing Schools: Michigan (Ross) - Class of 2014 GMAT 1: 730 Q49 V39 GPA: 3.13 WE: Corporate Finance (Aerospace and Defense) Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink] ### Show Tags 10 Dec 2010, 06:20 1 This post received KUDOS I say D as well. Great explanation _________________ Kudos [?]: 47 [1], given: 46 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7791 Kudos [?]: 18108 [1], given: 236 Location: Pune, India Re: If the average (arithmetic mean) of n consecutive odd [#permalink] ### Show Tags 29 Sep 2012, 22:41 1 This post received KUDOS Expert's post bandgmat wrote: I think solution D is wrong, what is numbers are : -5, -3, -1, 1, 3,5,7, 9 then range is 14 thus least value in set is : -5 However, if we consider numbers from 3 to 11 then least value is 3. Yeah, but is the average of these numbers 10? _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 18108 [1], given: 236

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135410 [1], given: 12692

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

### Show Tags

07 Jul 2013, 23:54
1
KUDOS
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

To find DS questions by Kudos, sort by Kudos here: gmat-data-sufficiency-ds-141/
To find PS questions by Kudos, sort by Kudos here: gmat-problem-solving-ps-140/

_________________

Kudos [?]: 135410 [1], given: 12692

Intern
Joined: 05 May 2013
Posts: 27

Kudos [?]: 23 [1], given: 5

GMAT 1: 730 Q50 V39
GRE 1: 1480 Q800 V680
Re: If the average (arithmetic mean) of n consecutive odd [#permalink]

### Show Tags

09 Jul 2013, 06:30
1
KUDOS
Let a be the first term. every term in this sequence can be expressed as a+ (i-1) where i ranges from 1 to n. Thus sum of these terms is a*n +1+2+3+..+n-1= an +n(n-1)/2 = 10 n.

(1) We are given that a+n-1 -a =14. We have two eqns for the unkowns (a and n ) and thus (1) is sufficient. No need to actually solve for and and n.

(2) is also sufficient since it is given a+(n-1) =17.

Kudos [?]: 23 [1], given: 5

Manager
Joined: 15 Apr 2011
Posts: 68

Kudos [?]: 21 [0], given: 45

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

### Show Tags

14 Apr 2012, 10:11
Awesome explanation Bunuel!
_________________

Kudos [?]: 21 [0], given: 45

Intern
Joined: 05 Sep 2012
Posts: 1

Kudos [?]: [0], given: 8

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

### Show Tags

29 Sep 2012, 22:27
I think solution D is wrong, what is numbers are : -5, -3, -1, 1, 3,5,7, 9 then range is 14 thus least value in set is : -5
However, if we consider numbers from 3 to 11 then least value is 3.

Kudos [?]: [0], given: 8

Manager
Joined: 11 Jul 2012
Posts: 55

Kudos [?]: 53 [0], given: 25

GMAT 1: 650 Q49 V29
Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]

### Show Tags

28 Oct 2012, 10:36
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Doesn't the highlighted statement actually mean that the highest number in the series is 17??

Kudos [?]: 53 [0], given: 25

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7791

Kudos [?]: 18108 [0], given: 236

Location: Pune, India
Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]

### Show Tags

29 Oct 2012, 01:26
avaneeshvyas wrote:
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Doesn't the highlighted statement actually mean that the highest number in the series is 17??

Yes. We generally use the terms greatest/largest.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18108 [0], given: 236

Intern
Joined: 24 Apr 2013
Posts: 1

Kudos [?]: [0], given: 2

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

### Show Tags

09 Jul 2013, 20:57
Or, since this is DS, we can skip the math and use the fact that for a consecutive sequence we only need 2 pieces of information (among mean, smallest number, greatest number, and range) to determine it. So D is correct.

Kudos [?]: [0], given: 2

Manager
Joined: 24 Jun 2014
Posts: 52

Kudos [?]: 23 [0], given: 97

Concentration: Social Entrepreneurship, Nonprofit
Re: If the average (arithmetic mean) of n consecutive odd [#permalink]

### Show Tags

28 Feb 2015, 21:19
As per the question average of n consecutive integers is 10 ;Sum of n consecutive integers =10n
or lets say lowest integer is k then k+ k+2+k+4...+ k+2(n-1) =10n
Simplifying further nk+2(1+2...+n-1)=10n ----> A

lets go with option I

i) The range of n integers is 14

so we know highest integer - lowest integer =14
highest integer =k+2(n-1)
lowest integer =k

Hence we get 2(n-1) =14 or n=8 ,Substituting we get value of k hence I is sufficient

ii) if greatest integer is 17,
then sum would be 17 + 17-2 ...+(17 -(n-1)) = 10n
Simplifying 17n - 2(1+2...+(n-1))=10n or 7n = 2(1+2+...+(n-1))----> B

From A and B we get K=3 ,this sufficient to get all numbers in series Hence II is sufficient

Kudos [?]: 23 [0], given: 97

Intern
Joined: 10 Mar 2015
Posts: 2

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

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

### Show Tags

09 Oct 2015, 04:43
Below is a very simple logical approach to the problem.

Set={consecutive odd integers} for eg:{3,5,7}---Avg=5(an odd number;this is because number of integers in set= odd)
Avg given=10 (even number)
Thus, obviously the number of terms are even. For eg: {9;11} or {7,9,11,13} Avg:10
Thus; possible entries in set={1,3,5,7,9,11,13,15,17}

1) range=Greatest-least= 14
Check set above ;only 17-3=14 ; thus highest number is 17,lowest 3-- Sufficient

2) Greatest =17
in consecutive integer set greatest+lowest/2= mean
17+Low/2=10
Low= 3 ~~ sufficient.

ANS= D
Hope I was clear.

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

Current Student
Joined: 12 Jul 2013
Posts: 7

Kudos [?]: [0], given: 84

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

### Show Tags

23 Oct 2016, 02:48
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Bunuel ,

My question is from the problem statement itself only one solution is possible. [ 3,5,7,9,11,13,15,17]. Are there any chances to encounter such a question on actual exam

Kudos [?]: [0], given: 84

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135410 [0], given: 12692

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

### Show Tags

23 Oct 2016, 05:32
rt1601 wrote:
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Bunuel ,

My question is from the problem statement itself only one solution is possible. [ 3,5,7,9,11,13,15,17]. Are there any chances to encounter such a question on actual exam

Unfiniftley many sets are possible:
{9, 11}
{7, 9, 11, 13}
{5, 7, 9, 11, 13, 15}
...
_________________

Kudos [?]: 135410 [0], given: 12692

Manager
Joined: 23 Dec 2013
Posts: 235

Kudos [?]: 16 [0], given: 21

Location: United States (CA)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: If the average (arithmetic mean) of n consecutive odd [#permalink]

### Show Tags

02 Jun 2017, 08:43
tonebeeze wrote:
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"

The goal is to find the minimum value of the set of n consecutive odd integers whose average is 10.

Statement 1) The range of n integers is 14.

If you know the average and range of a set of consecutive integers, then you can determine its length and the value of each element in that set. So there is only one set of consecutive odd integers with an average of 10 and a range of 14. Sufficient.

Statement 2) The max of n integers is 17.

Once again, if we know the maximum value and the average of a set of evenly spaced integers, then we can determine all values of that set. Sufficient.

Kudos [?]: 16 [0], given: 21

Manager
Joined: 19 Aug 2016
Posts: 64

Kudos [?]: 3 [0], given: 1

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

### Show Tags

07 Sep 2017, 18:19
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Hi Bunuel

Could you please explain what evenly spaced set means?

Kudos [?]: 3 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 42575

Kudos [?]: 135410 [0], given: 12692

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

### Show Tags

07 Sep 2017, 20:39
zanaik89 wrote:
Bunuel wrote:
tonebeeze wrote:
Hello All,

I got this problem correct. I just would like to see a technical explanation of how to arrive at both occasions of sufficiency.

Thanks!

"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"

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.

Hi Bunuel

Could you please explain what evenly spaced set means?

Evenly spaced set (aka arithmetic progression) is a special type of sequence in which the difference between successive terms is constant. Fore example, 1, 4, 7, 10, ... is an evenly spaced set. Check for more here: https://gmatclub.com/forum/math-sequenc ... 01891.html

Hope it helps.
_________________

Kudos [?]: 135410 [0], given: 12692

Re: If the average (arithmetic mean) of n consecutive odd   [#permalink] 07 Sep 2017, 20:39
Display posts from previous: Sort by