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# Is the average (arithmetic mean) of a certain series of

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Intern
Joined: 02 Nov 2009
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Is the average (arithmetic mean) of a certain series of [#permalink]

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18 Apr 2010, 13:45
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71% (01:27) correct 29% (01:00) wrong based on 17 sessions

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Is the average (arithmetic mean) of a certain series of consecutive integers an integer?

(1) The number of terms in the series is even.

(2) The median of the terms in the series is not an integer.

[Reveal] Spoiler:
D
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18 Apr 2010, 13:58
1
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IMO D

Statement 1. if number of terms is even , AM cannot be integer, hence sufficient.

take eg of 1,2,3 and 1,2,3,4

sum = n(A+L)/2 here d=1
AM = (A+L)/2 , now if A is odd , and its having even terms then L is even and vice versa .
Hence AM is not an integer.

Statement 2. if median is not an integer then , it cannot have odd number of terms, it must have even number of terms.. hence sufficient.

Thus D
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18 Apr 2010, 19:03
sudai wrote:
Is the average (arithmetic mean) of a certain series of consecutive integers an integer?
(1) The number of terms in the series is even.

(2) The median of the terms in the series is not an integer.

[Reveal] Spoiler:
D

statement 1:sum of series is given by: S = n/2[2a+(n-1).d]
hence arithmetic mean A.M.= S/n => 1/2[2a+(n-1)] as d=1( consecutive integer)
=> A.M.= a+(n-1)/2
now, since n is even so n-1 is odd hence (n-1)/2 will not be integer => hence A.M. will not be an integer ....suff.

2nd statement: as gurpreetsingh has mentioned ...suff.
hence both statements are sufficient to answer.
Re: Math   [#permalink] 18 Apr 2010, 19:03
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