If a, b, and c are integers such that a(b + c) is an odd integer, which of the following e… — GMAT

If $a$ , $b$ , and $c$ are integers such that $a(b + c)$ is an odd integer, which of the following expressions MUST be an even integer?

The expression

a + b + c

must be an even integer.

For the product

a(b + c)

to be odd, both

a

and

(b + c)

must be odd integers. Regrouping the sum

a + b + c

a + (b + c)

shows it is the sum of two odd integers, which is guaranteed to be an even integer.

Analyze the condition

a(b + c)

is odd

For a product of two integers to be odd, both factors must be odd. Therefore,

a

is odd and

(b + c)

is odd.

The product of an even integer and any integer is always even.

Evaluate the parity of

a + b + c

a + b + c = a + (b + c) = \text{odd} + \text{odd} = \text{even}

The sum of any two odd integers is always an even integer.

Parity rules for integer addition and multiplication

Question