OG_DS_73, Stuck on zero

[mathelites]

Hello forum,

I am having an issue figuring out this question#73, data sufficiency, from OG 12th edition:


If m is an integer, is m odd?

(1) m/2 is not an even integer
(2) m-3 is an even integer


The solution in the book considers (1) to not be sufficient, which I agree with.

Next, the solution solves m-3 out to consider for some integer k, that m-3 = 2k and m = 2(k+1)+1. Then for any integer k, m will be an odd integer.

However, if you consider m is the integer 3, then (m-3) = 0. Which is not an even integer. I think I may be confusing myself here but maybe an expert here can sort me out!

[NikolayZ]

Hey there.

In DS you need to take statements as TRUE. And you have to pick numbers so that the statement remains true.

In this case.
stmt 2) you can not pick 3, because 3-3=0 (0 is an even integer)
For m-3 to be even, m must be odd. Because odd+odd and odd-odd is even.

[Testluv]

Hi mathelites,

(love the name!)

zero is indeed an even integer as it falls between two odd integers on the number line.

Other facts about zero: it is neither positive nor negative. It is a multiple of every (other) number but a factor of none.