Are negative numbers divisible by 2 considered even numbers?

Question

This is probably a stupid question, but on the gmat, are numbers like -2, -4, -6, etc considered even? How about 0 - is it even, odd, or neither?

If 0, and negative numbers can be considered even, then (1) alone is sufficient. If not, then (1) and (2) together are sufficient to answer the question.

Bunuel · Answer

1. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2,  0 , 2, 4, ... are all even integers.

2. An odd number is an   integer   that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.

3. Zero is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

abhinavsodha800 · Answer

Hi Bunuel,
Zero is divisible by 3 also then why it is not an odd number ? Also in question it confuses me lot when it is written like positive integer or positive even integer ? i am not able to figure when to consider zero or not

avigutman · Answer

Zero is divisible by everything (therefore yes it’s even and yes it’s a multiple of 3). It is an integer. It is neither positive nor negative. 
I think the source of your confusion is a misunderstanding of the words even and odd. Even means multiple of 2. Odd means not a multiple of 2. 
Is a multiple of 3 odd? Depends which multiple of 3. Looking at the number line, multiples of 3 alternate between odd and even. 
Divisibility by 2 and divisibility by 3 have nothing to do with each other.

Posted from my mobile device

abhinavsodha800 · Answer

i am aware that anything which is divided by 2 is even and by 3 it is odd. since is zero is divided by both so it is nether odd or even. it is only an positive integer but when question asks positive even integer i get confused . many times i have missed considering zero in question. so do i need to consider zero in both cases (positive integer and positive even integer). For positive integer i understood but why for positive even integer since zero is neither even nor odd.

chetan2u · Answer

You are getting it wrong..

0 is neither positive nor negative.
As far as the concept of even and odd is considered, it is connected ONLY with division by 2.
If divisible by 2, it is even. If not divisible by 2, it is odd.

0 is divisible by 2, so it is even. In the same way as 6, which is divisible by 3 but is even.

Fact : 0 is even, but is neither positive nor negative.

Bunuel · Answer

Not all integers that are divisible by 3 are odd. For example, -12, -6, 0, 6, 12, 18, ...

Mathpromax · Answer

Thank you all i have gained something from your answere

Are negative numbers divisible by 2 considered even numbers?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards