Question

Let $o$ be an odd whole number and let $n$ be any whole number. Which of the following statements about the whole number $o^2 + no$ is always true?

it is always odd

it is always even

it is even only if $n$ is even

it is odd only if $n$ is odd

it is odd only if $n$ is even

Solution:

Factor $o^2 + no = o(o + n).$ Because $o$ is odd, the product is odd exactly when $o + n$ is odd, which happens only when $n$ is even. When $n$ is odd, $o + n$ is even and the product is even.

So the number is odd only if $n$ is even.

Thus, the correct answer is E .

1986 AMC 8 Problem 17

Solution:

Problem 17 in Other Years