If x and y are positive integers, is the product xy divisible by 4? (1) x is divisible by … — GMAT

If $x$ and $y$ are positive integers, is the product $xy$ divisible by 4?

(1) $x$ is divisible by 4.
(2) $x + y$ is an odd integer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Answer
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.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The correct answer is that Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) establishes that

x

is a multiple of 4, so any integer product

xy

must also be a multiple of 4. Statement (2) only guarantees that one of

x

y

is even, which is not enough to determine if the product has two factors of 2.

Analyze the question stem target

We need to determine whether

xy

is divisible by 4, given that

x

and

y

are positive integers.

Establishing integer constraints ensures we evaluate divisibility conditions properly.

Evaluate Statement (1) independently

x

is divisible by 4, then

x = 4k

for some positive integer

k

. Then

xy = (4k)y = 4(ky)

, which is divisible by 4. This gives a definitive YES.

Multiplying any multiple of 4 by an integer results in a multiple of 4. Therefore, Statement (1) alone is sufficient.

Evaluate Statement (2) independently

x + y

is odd, one integer is even and the other is odd. Case 1: If

x = 4

and

y = 1

x+y=5

(odd) and

xy = 4

(divisible by 4 -> YES). Case 2: If

x = 2

and

y = 3

x+y=5

(odd) and

xy = 6

(not divisible by 4 -> NO).

Since Statement (2) yields both YES and NO outcomes, it alone is not sufficient.

Divisibility and Parity Rules in Data Sufficiency

Question