anonymous
  • anonymous
If a, b and c are odd integers, which of the following expressions must be an even integer? a + b + c a(b + c) ab + bc + ca a(b + c - 1)
Mathematics
chestercat
  • chestercat
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MePitt
  • MePitt
i think c
whovianchick
  • whovianchick
No, it's B. plug in odd numbers for all of the variables, and you get B every time
anonymous
  • anonymous
First fact needed: ODD + ODD = EVEN This is always true. And, ODD + EVEN = ODD. So, a + b + c is (ODD + ODD + ODD) = (ODD + ODD) + ODD = EVEN + ODD = ODD.

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anonymous
  • anonymous
anonymous
  • anonymous
Now, we need more facts. (EVEN)(EVEN) = EVEN and (EVEN)(ODD) = EVEN; that is, multiplying by an even number always given you an even number. Do you see how that can help you with a(b + c)?
anonymous
  • anonymous
anonymous
  • anonymous
I'll get you started: ODD(ODD + ODD) = ?
anonymous
  • anonymous
EVEN
anonymous
  • anonymous
RIght... ODD(ODD + ODD) = ODD(EVEN) = EVEN. Yep!
whovianchick
  • whovianchick
It's B, I've already answered. Plug in numbers, and you'll see I'm right
anonymous
  • anonymous
Now, how about the others? (Perhaps there is more than one that must always be even...)
KaylaRdz0405
  • KaylaRdz0405
i agree with whovianchick
anonymous
  • anonymous
Plugging in #s is a good approach. Sometimes it's useful to use some other ideas, too.
whovianchick
  • whovianchick
@OneMathCat The problem is already solved. Stop rambling.
anonymous
  • anonymous
Yep!! I do have a tendency to ramble ... sorry! Have a good day!
anonymous
  • anonymous
whovianchick
  • whovianchick
no prob :)

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