Data Sufficiency

aditya.j wrote:If A,B are non zero integers and A^8xB^4 - A^4xB 2= 12, which of the following could be A^2 in terms of B?

I. 2/B
II. - 2/B
III. 3/B

:roll: [/spoiler]

While you don't need to here, I'd find it easiest to factor first. We can take out the common factor of a^4 * b^2 from each expression, then use a difference of squares:

(a^8)(b^4) - (a^4)(b^2) = 12
(a^4)(b^2) [ (a^4)(b^2) - 1] = 12
(a^2 * b)^2 [ (a^2)(b) + 1 ] [ (a^2)(b) - 1 ] = 12

You could use divisibility properties here (each term on the left side needs to be a divisor of 12, so there are almost no possibilities to consider), but I think the easiest thing to do is to simply plug in each answer choice. If you replace a^2 with 2/b or with -2/b, the left side is equal to 12. If you replace a^2 with 3/b, then the left side is much larger than 12. So the answer is I and II only.