Yes!
An odd number divided by 2 must leave a remainder 1.
An even number should be divisible by 2.
No other real number outside this view can be called odd or even.
Odd or Even only for integers?
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
-
fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
vineeshp´s answer is correct. Let me say a bit more on this matter: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?
"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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
