Can we assume k to be an Integer?

[messi10]

Hello,

My query is pertaining to the question in the Number Properties guide (4th Edition) on page 52 under the chapter Consecutive Integers.

Its a DS question that asks:
Is k square odd?
1) k - 1 is divisible by 2
2) The sum of k consecutive integers is divisible by k

My doubt is with statement 1. I understand that the question is there to help understand the concept at hand but if this question were an actual GMAT question, then can we ignore that it has not been specified in the question or the statement whether k is an integer.

If k can be a non integer then statement 1 is insufficient.

Thanks for the help

[tim]

can you give us a non-integer k such that k-1 is divisible by 2? if not, then statement 1 requires k to be an integer..

[messi10]

Hi Tim,

Thanks for the quick response.

If k is a decimal number such as 2.2 then it is divisible by 2

[RonPurewal]

If k is a decimal number such as 2.2 then it is divisible by 2

nope. if a number is "divisible by 2", then, by definition, it is an integer multiple of 2.
a similar definition obtains for any other divisor (i.e., there's nothing special about dividing specifically by 2).

so, in statement 1, (k - 1) has to be an integer multiple of 2 (i.e., an even integer).