Question

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)

Answer 1

i think c

Answer 2

No, it's B. plug in odd numbers for all of the variables, and you get B every time

Answer 3

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.

Answer 4

@KaylaRdz0405

Answer 5

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)?

Answer 6

@TINY10207

Answer 7

I'll get you started: ODD(ODD + ODD) = ?

Answer 8

EVEN

Answer 9

RIght... ODD(ODD + ODD) = ODD(EVEN) = EVEN. Yep!

Answer 10

It's B, I've already answered. Plug in numbers, and you'll see I'm right

Answer 11

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

Answer 12

i agree with whovianchick

Answer 13

Plugging in #s is a good approach. Sometimes it's useful to use some other ideas, too.

Answer 14

@OneMathCat The problem is already solved. Stop rambling.

Answer 15

Yep!! I do have a tendency to ramble ... sorry! Have a good day!

Answer 16

THANK U @whovianchick

Answer 17

no prob :)