shebinjs wrote:Hi,
Just a quick question.
Do we tell odd or even only for integers? Say for e.g. I got 0.5 as the value for a variable. Is it odd or even?
vineeshp´s answer is correct. Let me say a bit more on this matter:
"Divisibility is an integer business" in the sense that if (say) one of the statements of a data sufficiency problem tells you that "A is divisible by B", you can (AND SHOULD) admit that A and B are integers.
Corollary (that is, a consequence of above): when a number is said/given as:
> "odd" that means that it is an INTEGER that leaves 1 as the remainder when it is divided by 2 ;
> "even" that means that it is an INTEGER that leaves 0 as the remainder(*) when it is divided by 2 ;
(*) Many prep companies/books/teachers usually say "there is no remainder" when they should say "the remainder is zero", by the way.
> any given integer is necessarily odd or even, and it cannot be both.
Important: zero is even, because when 0 is divided by 2 we have (quotient 0 and) remainder 0.
In summary:
(1) All integers are divided into 2 groups -- ODDs and EVENs -- and no integer is at both groups ;
(2) All ODD numbers are necessarily integers and the same can be said about the EVEN numbers.
Curiosity: people (and the GMAT) say "Let n be an even integer" when they could simply say "Let n be an even number" or, more succint, "Let n be even."
Important: if you know a certain (real) number A is not even, it does NOT need to be odd, because it could be non-integer! In other words:
(1) Integers that are NOT even are NECESSARILY odd (and vice-versa) ;
(2) Any given (real) number is EXACTLY one of three possibilities: odd, even, non-integer.
Regards,
Fabio.
