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anonymous

  • one year ago

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)

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  1. MePitt
    • one year ago
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    i think c

  2. whovianchick
    • one year ago
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    No, it's B. plug in odd numbers for all of the variables, and you get B every time

  3. anonymous
    • one year ago
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    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.

  4. anonymous
    • one year ago
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    @KaylaRdz0405

  5. anonymous
    • one year ago
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    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)?

  6. anonymous
    • one year ago
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    @TINY10207

  7. anonymous
    • one year ago
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    I'll get you started: ODD(ODD + ODD) = ?

  8. anonymous
    • one year ago
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    EVEN

  9. anonymous
    • one year ago
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    RIght... ODD(ODD + ODD) = ODD(EVEN) = EVEN. Yep!

  10. whovianchick
    • one year ago
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    It's B, I've already answered. Plug in numbers, and you'll see I'm right

  11. anonymous
    • one year ago
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    Now, how about the others? (Perhaps there is more than one that must always be even...)

  12. KaylaRdz0405
    • one year ago
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    i agree with whovianchick

  13. anonymous
    • one year ago
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    Plugging in #s is a good approach. Sometimes it's useful to use some other ideas, too.

  14. whovianchick
    • one year ago
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    @OneMathCat The problem is already solved. Stop rambling.

  15. anonymous
    • one year ago
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    Yep!! I do have a tendency to ramble ... sorry! Have a good day!

  16. anonymous
    • one year ago
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    THANK U @whovianchick

  17. whovianchick
    • one year ago
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    no prob :)

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