Data Sufficiency

rintoo22 wrote:If the sum of three integers is even, is the product of the three integers a multiple of 4 ?
(1) All three integers are equal.
(2) All three integers are even.

The answer is, indeed, D. I'm not sure why the resource would say the answer is B.

Target question: Is the product of the three integers a multiple of 4 ?

Let's let the 3 numbers be w, x and y.

Statement 1: All three integers are equal.
This means that the 3 integers are either all odd or all even. Let's consider each case.

Case a: all 3 integers are odd
Odd + Odd + Odd = Odd. So it cannot be the case that all 3 are odd.

Case b: all 3 integers are even
even + even + even = even. So it must be the case that all 3 are even.

IMPORTANT: If an integer is divisible by 2, then it can be rewritten as (2)(some integer)

So, the product wxy can be rewritten as follows.

wxy = (2)(some integer)(2)(some integer)(2)(some integer)
= 8(some integer)

This tells us that wxy is divisible by 8, which means it must also be divisible by 4.
In other words wxy must be a multiple of 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: All three integers are even.
Statement 2 provides the same information that statement 1 does.
So, statement 2 must also be SUFFICIENT

Answer = D

Cheers,
Brent

You're right in that -6 is not a multiple of 4, but that's not what the question says. It says the product is a multiple of 4. Here the product is -8 and -8 is a multiple of 4.

Cheers,
Brent