If x and y are positive integers, is the product xy divisible by 9?

(1) The product xy is divisible by 6.

(2) x and y are perfect squares.

the answer is c for this

I have a doubt

Given information from the question stem: x and y are positive integers.

Statement 1: The product xy is divisible by 6. This tells you that 3 and 2 are factors

of xy. However this statement is not sufficient alone. Conceptual understanding

will tell you that if 3 is a factor of xy then it is possible that 9 is also a factor of

xy. However it is equally possible that 9 is not a factor of xy. If you are in doubt

you can use numbers and Play Devil’s Advocate. xy could equal 6 or 12, both

of which are divisible by 6 as the statement requires and are not multiples of 9.

This would yield an answer of “no.” xy could also equal 36, which is a multiple of

6 and also of 9. This would yield the answer of “yes.” Since yes and no answers

are both possible this statement is not consistent and is therefore not sufficient.

Eliminate choices A and D.

Statement 2: x and y are perfect squares. Conceptually this is clearly notsufficient. While each of the number must be a perfect square this statement

does not guarantee that the result will even be a multiple of 3, much less of 9.

Eliminate choice B.

Together: Statement 1 tells you that xy must include the prime factors of 2 and 3

(in order to be a multiple of 6). Since Statement 2 requires x and y to be perfect

squares the only way to have a 2 and a 3 as prime factors of x and y is to have

22 and 32 as factors of x and y. In fact, the smallest values for x and y are 4 and

9. So the answer to the question “Is xy divisible by 9?” is “yes.” Together the

statements yield one consistent answer and the correct answer is C.

but when we consider C

WE CAN GET MULTIPLE VALUES SUCH AS 36,9 & 4,9AS WE ARE GETTING MULTIPLE VALUES SHOULDN'T THE ANSWER BE

ECAN SOMEONE PLEASE HELP

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