PowerPrep Evens and Odds Question

[mrsultanmehmood]

3) If x and y are integers and x = 50y + 69, which of the following must be odd. (other than plugging in/faster method?)

A xy
B x+y
C x+2y
D 3x-1
E 3x+1

[tommywallach]

Hey mr. Sultan,

I can answer your third question here.

Whenever you get an evens and odds question, all you have to do is worry about whether or not stuff is even or odd.

3) If x and y are integers and x = 50y + 69, which of the following must be odd. (other than plugging in/faster method?)

50y will be even no matter what (because 50 is even), and 69 is odd. An even + an odd = an odd.

So we know that x is odd, and we don't know anything about y.

A xy -- If y is even, this will not be odd.
B x+y -- If y is odd, this will be odd + odd = even
C x+2y -- x is odd, and 2y is even (no matter what y is), so this will always be odd -- CORRECT
D 3x-1 -- Because x is odd, 3x is odd. An odd - 1 = even
E 3x+1 -- Same logic as D

Does that help? No need to plug in actual numbers, just know your even/odd multiplication/addition/subtraction rules.

-t

[mrsultanmehmood]

Thanks! It indeed helps!!!

[tommywallach]

Glad to help!

-t