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Are -2 or -4 or -6 ... even numbers?

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by GMATGuruNY » Sun Sep 04, 2016 2:05 am
george.kaipanat wrote:Hi,

Maybe im being stupid, but seriously, Are -2 or -4 or -6 ... (-ve numbers when divided by 2 gives remainder 0) even numbers?

Thanks,

George
From the OG:
Any integer that is divisible by 2 is an even integer; the set of even integers is {. . . -4, -2, 0, 2, 4, 6, 8, . . .}.
Integers that are not divisible by 2 are odd integers; {. . . -3, -1, 1, 3, 5, . . .} is the set of odd integers.
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by [email protected] » Sun Sep 04, 2016 11:44 am
Hi george.kaipanat,

An easy way to remember certain Number Property rules is to think about how a number line "works." When you go in EITHER direction on a number line, the integers follow a pattern: odd - even - odd - even.... etc.

2 = even
1 = odd
0 = even
-1 = odd
-2 = even
-3 = odd
etc.

So the answer to your question is YES: -2, -4, -6 etc. ARE even integers.

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by Brent@GMATPrepNow » Sun Sep 04, 2016 4:33 pm
george.kaipanat wrote:Hi,

Maybe im being stupid, but seriously, Are -2 or -4 or -6 ... (-ve numbers when divided by 2 gives remainder 0) even numbers?

Thanks,

George
Another way to look at evens and odds:

An EVEN integer is any integer that can be expressed as the product 2k, where k is an integer.
So, -6 is an even integer, since -6 = 2(-3)
And 0 is an even integer, since 0 = 2(0)

An ODD integer is any integer that can be expressed as 2k + 1, where k is an integer.
So, 9 is an odd integer, since 9 = 2(4) + 1
Likewise, -11 is an odd integer, since -11 = 2(-6) + 1

For more on ODD and EVEN, see this video: https://www.gmatprepnow.com/module/gmat ... /video/837

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by Matt@VeritasPrep » Thu Sep 15, 2016 8:01 pm
Here's the test:

Even/2 = Integer

So if x is even, x/2 will = an integer.

-2/2 = -1, an integer, so that works!

-4/2 = -2, an integer, so that works!

-6/2 = -3, an integer, so that works!

etc.
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