If i and j are integers, is

If i and j are integers, is i+j an even integer?

2 Explanations

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Carlson Rainer

Hi - for statement two could you assume that if i+j is even, and we know that i=j, could you assume that any even + even or odd+odd would in fact be an even result? That is how I came up with my reasoning.

Jan 7, 2017 • Comment

Sam Kinsman

Hi Carlson,
Yes, that's right.

even + even = even
odd + odd = even

Therefore, if i=j, then the result of i+j must be even.

Jan 11, 2017 • Reply

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Mike McGarry, Magoosh Tutor

Aug 17, 2015 • Comment

Stephen Mortensen

"Two times anything is even" should instead have been said "2 times any integer is even." 2 * 1.5 = 3, which is odd.

May 11, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Stephen,

Thanks for pointing this out. You're completely right that the statement "2 times any integer is even" is more accurate. However, since we are told in the prompt that both i and j are integers, the statement in the explanation video is justified within the context of the question. That said, I've let the content editors know about the wording. However, since we are a small group with many projects in progress, it may be a while before the video is updated.

Thanks, again, for taking the time to tell us about this! :)

May 12, 2016 • Reply