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

Question

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  D

please explain why the second statement is sufficient.
Thanks

Aleehsgonji · Answer

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.

So answer is D

GMAT TIGER · Answer

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...

gmate2010 · Answer

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

thb · Answer

Thanks for explaining the 2nd property. That was my missing part...

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

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