Do we I have to inter that **x**/**y** can’t be **0** for the following question?

If they can be **0**, then **xy** also becomes divisible by **48** as **0** is divisible by any non-zero number.

“must be true”

1 is true for all cases

2 is true only when x and y both are 0

y can never be 0 for 3

@vidishas99, I haven’t asked for answers. I’ve asked whether I’ve to infer that x/y is positive integer or not. The book’s solution infers that they’re positive integers. Hence, the first one is only right answer.

They can be negative and zero too, answer will not change

The concept they are testing here is of factors and multiple .

**Given:**

x is divisible by 18(18 is a factor of x) and 18 = 2 x 3^2 —> At minimum x must contains one 2 and two 3’s

y is divisible by 12(12 is a factor of y) and 12 = 2^2 x 3 —> At minimum y must contain two 2’s and one 3

Now,

Statement A → x+y is divisible by 6 (2x3)—> Always **true** as we can make a 6 from factors of x and y.

Statement B —> xy is divisible by 48 (2^4 x 3) —> We can’t says always(must) as we know that x and y contains three 2’s in total and we can’t say that it will surely have another two in their factor so this statement is also **false**.

Statement C x/y —> (2 x 3^2 ) **/** (2^2 x3) —> 3/2 ----> Not even an integer , hence this is also **false**.

Answer → A

Thank you @vidishas99 & @HoldMyBeer for your explanations. I think the concept “**a** is divisible by **b**” means that the remainder will be zero if we divide **a** by **b**.

@vidishas99, you’re right. They can be anything: negative, zero or positive and the answer doesn’t change for it. I made mistake by skipping the “**must be true**” statement & became confused!

Yeah , it a pretty common topic tested in GRE that x/y = integer (x is a multiple of y and y is a divisor of x )