DS (Number Sysytem)

[rintoo22]

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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My Solution.

the sum of three integers is even

.
Therefore OEO and EEE can be the options.
According to Statement 1, if all 3 integers are equal then EEE can be the only option. So the product of the three integers is a multiple of 4.

SUFFICIENT

According to Statement 2, if all 3 integers are even then EEE can be the only option. So the product of the three integers is a multiple of 4.

SUFFICIENT

Answer should be D. However the answer given is B.
Where am I going wrong ?

[Brent@GMATPrepNow]

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

[killerdrummer]

Brent - Have this doubt and wanted to clear it.



What if all the numbers are negative as in -2 ,-2, -2.Their sum is even i.e. -6 but is -6 multiple of 4? I am not sure of that..

[Brent@GMATPrepNow]

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

[killerdrummer]

Gotcha!

Thanks Brent for prompt response.