shreya32 wrote:

Is integer (x^2)*(y^4) divisible by 9?

x is an integer divisible by 3

xy is an integer divisible by 9

My thinking was that:

if 3 is a factor of x, than x^2 will have atleast 2 3's as its prime factors - so x^2 is divisible by 9, so the entire expression will be divisible by 9 - statement 1 is sufficient.

if xy is divisible by 9, then the expression can be rewritten as (xy)*(x*(y^3)) = 9m(x*(y^3)) which is divisible by 9 - statement 2 is sufficient.

But the answer is that both statements are not sufficient together..what am i doing wrong? fyi - this question is one of the gmatclub flashcards

Probably, the thing that confused you was that \(x^2*y^4\) is an integer (given in the question stem) and stmnt 1 says that x is an integer. One might feel that it implies that y is also an integer. This is the reason number properties questions are tricky.

Say, x = 81, y = 1/9

x is an integer divisible by 3.

\(x^2*y^4 = 81*81*(1/9)*(1/9)*(1/9)*(1/9) = 1\) is an integer.

But y is not an integer and \(x^2*y^4\) is not divisible by 9.

Using the same example, you can see why both the statements together are not sufficient.

x = 81, y = 1/9

x is an integer divisible by 3.

\(x^2*y^4 = 81*81*(1/9)*(1/9)*(1/9)*(1/9) = 1\) is an integer.

xy = 81*(1/9) = 9 is an integer divisible by 9.

But \(x^2*y^4\) is not divisible by 9.

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