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# is k^2 odd? 1) k-1 is divisable by 2 2) the sum of K

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Intern
Joined: 16 May 2009
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is k^2 odd? 1) k-1 is divisable by 2 2) the sum of K [#permalink]

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31 Aug 2009, 11:21
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is k^2 odd?

1) k-1 is divisable by 2
2) the sum of K consecutive integers is divisable by K

O.A is
[Reveal] Spoiler:
D

please explain why the second statement is sufficient.
Thanks
Manager
Joined: 10 Jul 2009
Posts: 165
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Kudos [?]: 106 [0], given: 8

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31 Aug 2009, 11:30
From the second statement K cannot be an even number as sum of K consecutive numbers will always be odd when K is even and odd number cannot be divided by even number. Substitute an odd number in place of K
Sum of 5 consecutive numbers = 13 + 14+15+16+17 = 75 is divisible by 5
Sum of 7 consecutive numbers = 8+9+10+11+12+13+14 = 77 is divisible by 7
So statement 2 alone is sufficient to conclude K is odd and hence K^2 is odd.

SVP
Joined: 29 Aug 2007
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31 Aug 2009, 13:08
Pedros wrote:
is k^2 odd?

1) k-1 is divisable by 2
2) the sum of K consecutive integers is divisable by K

O.A is
[Reveal] Spoiler:
D

please explain why the second statement is sufficient.
Thanks

This is important concept: Only if number of consecutive integers (K) is odd, the sum of such consecutive integers (K) is divisible by that number (K).
Therefore B is suff...
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Manager
Joined: 25 Aug 2009
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31 Aug 2009, 13:57
k^2 will be odd if k is odd..So, the question is asking if k is odd..

1.) k -1 is divisible by 2

=> k - 1 is even

=> k is odd..Sufficient

2.) Property:- Sum of odd consecutive numbers is divisible by the number of integers..Please remember this..This is the second question which I have seen using this property.

Since, sum of k consecutive integers is divisible by k

=> k is odd..Sufficent..

or you can plug numbers if you don't remember this property..

Let k = 2,3,4

Case1: Sum = 1 + 2 = 3 ( not divisible by 2)

Case2: sum = 1 + 2 + 3 = 6 divisible by 3

Case3: Sum = 1 + 2 + 3 + 4 = 10 not divisible by 4

Hence, k should be odd..Sufficient

Hence, D
Intern
Joined: 30 Aug 2009
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31 Aug 2009, 22:14
Thanks for explaining the 2nd property. That was my missing part...
Re: Divisability   [#permalink] 31 Aug 2009, 22:14
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