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

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If the average (arithmetic mean) of n consecutive odd [#permalink]  09 Dec 2010, 14:43
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58% (02:04) correct 41% (00:59) wrong based on 121 sessions
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"
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]  09 Dec 2010, 14:59
13
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"

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.

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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]  10 Dec 2010, 06:20
1
KUDOS
I say D as well.

Great explanation
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]  12 Dec 2010, 04:24
5
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.
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews SVP Joined: 16 Nov 2010 Posts: 1698 Location: United States (IN) Concentration: Strategy, Technology Followers: 29 Kudos [?]: 265 [1] , given: 36 Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink] 06 Apr 2011, 07:28 1 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) Manager Joined: 15 Apr 2011 Posts: 71 Followers: 0 Kudos [?]: 13 [0], given: 45 Re: If the average (arithmetic mean) of n consecutive odd [#permalink] 14 Apr 2012, 10:11 Awesome explanation Bunuel! _________________ Intern Joined: 05 Sep 2012 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 8 Re: If the average (arithmetic mean) of n consecutive odd [#permalink] 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4192 Location: Pune, India Followers: 897 Kudos [?]: 3816 [1] , given: 148 Re: If the average (arithmetic mean) of n consecutive odd [#permalink] 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 Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]  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??
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Re: Quant Rev v.2, DS # 66: Consecutive Integer Problem [#permalink]  29 Oct 2012, 01:26
Expert's post
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.
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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]  07 Jul 2013, 23:54
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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]  09 Jul 2013, 06:30
1
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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.

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Re: If the average (arithmetic mean) of n consecutive odd [#permalink]  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.
Re: If the average (arithmetic mean) of n consecutive odd   [#permalink] 09 Jul 2013, 20:57
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