Question

If a is an odd integer and b is an even integer, which of the following makes an odd integer?

A.) 3b
B.) a+3
C.) 2(a+b)
D.) a+2b
Explain your answer

Answer 1

9514 1404 393

Answer:

D.) a+2b

Explanation:

The integers 'a' and 'b' can be any, so you can choose a couple and evaluate these expressions to see what you get. For example, we can let a=1 and b=0. For these values, the offered expressions evaluate to ...

A) 3(0) = 0 . . . even

B) 1 +3 = 4 . . . even

C) 2(1+0) = 2 . . . even

D) 1 +2(0) = 1 . . . odd

_____

Additional comment

These rules apply to even/odd:

• odd × odd = odd
• odd × even = even
• even × even = even
• odd + odd = even
• odd + even = odd
• even + even = even

Then A is (odd)(even) = even; B is (odd)+(odd) = even; C is (even)(whatever) = even; D = (odd)+(even) = odd.