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# If Z1, Z2, Z3,..., Zn is a series of n consecutive even integers

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Intern
Joined: 05 Mar 2017
Posts: 6
If Z1, Z2, Z3,..., Zn is a series of n consecutive even integers  [#permalink]

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31 Aug 2017, 13:12
2
2
00:00

Difficulty:

95% (hard)

Question Stats:

39% (02:07) correct 61% (02:27) wrong based on 56 sessions

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If $$z_1$$, $$z_2$$, $$z_3$$,..., $$z_n$$ is a series of n consecutive even integers, is the sum of the integers in this series a perfect square?

1.) The median of the series is equal to $$4_n$$
2.) $$z_n$$ - $$z_1$$ = 12
Manager
Joined: 23 May 2017
Posts: 239
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: If Z1, Z2, Z3,..., Zn is a series of n consecutive even integers  [#permalink]

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31 Aug 2017, 14:31
3
Sum = Average * number of total items

Since the series is consecutive even number = median = average

[1] Average = 4n hence Sum = 4n * n = (2n)^2 - hence Sum is a perfect square

[2] - does not give any info on average
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Re: If Z1, Z2, Z3,..., Zn is a series of n consecutive even integers  [#permalink]

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09 May 2019, 07:51
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Re: If Z1, Z2, Z3,..., Zn is a series of n consecutive even integers   [#permalink] 09 May 2019, 07:51
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