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# What is the average (arithmetic mean) of a certain series of

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What is the average (arithmetic mean) of a certain series of [#permalink]

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20 Apr 2010, 07:22
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What is the average (arithmetic mean) of a certain series of N consecutive integers?

(1) The sum of the terms of the series is N.

(2) The sum of the greatest and least terms is 2.

[Reveal] Spoiler:
D

How should I solve this question? Thanks for your help!
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20 Apr 2010, 07:46
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sudai wrote:
What is the average (arithmetic mean) of a certain series of N consecutive integers?

(1) The sum of the terms of the series is N.

(2) The sum of the greatest and least terms is 2.

[Reveal] Spoiler:
D

How should I solve this question? Thanks for your help!

Arith. Mean of any series of consecutive integers = (a+l)/2 where a= first integer, l= last integer.
=> Sum of that series = (number of terms in the series)*(Average of the series) = N*(a+l)/2

Stmt 1) given, Sum= N => N*(a+l)/2= N => Mean = 1 => Sufficient info
Stmt 2) given, a+l= 2 => (a+l)/2 or the Mean = 1 => Sufficient info

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20 Apr 2010, 07:59
PhunsukWangdu wrote:
sudai wrote:
What is the average (arithmetic mean) of a certain series of N consecutive integers?

(1) The sum of the terms of the series is N.

(2) The sum of the greatest and least terms is 2.

[Reveal] Spoiler:
D

How should I solve this question? Thanks for your help!

Arith. Mean of any series of consecutive integers = (a+l)/2 where a= first integer, l= last integer.
=> Sum of that series = (number of terms in the series)*(Average of the series) = N*(a+l)/2

Stmt 1) given, Sum= N => N*(a+l)/2= N => Mean = 1 => Sufficient info
Stmt 2) given, a+l= 2 => (a+l)/2 or the Mean = 1 => Sufficient info

well explained! Thank you!
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Re: What is the average (arithmetic mean) of a certain series of [#permalink]

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05 Aug 2016, 22:17
Nice Question
See, the set of consecutive integers is always an AP
And for any AP series we have => Mean = Median = A(v)
Where A(v) = Average of any two terms for which the sum of their deviation around the mean is Zero.

Statement 1 => Sum of N terms N
Mean = N/N =1
Sufficient
Statement 2 => A(v) = 2/2 =1
Hence Mean =1
Alternatively => Sum of a AP series = N/2 [A+L] => Average = 1/2[first term + last term]
Sufficient

Smash That D

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Re: What is the average (arithmetic mean) of a certain series of   [#permalink] 05 Aug 2016, 22:17
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