If \(xy\ne 0,\) what is the value of \(\dfrac{x^4\cdot y^2-(xy)^2}{x^3\cdot y^2}?\)

[Gmat_mission]

If \(xy\ne 0,\) what is the value of \(\dfrac{x^4\cdot y^2-(xy)^2}{x^3\cdot y^2}?\)

(1) \(x = 2\)
(2) \(y = 8\)

Answer: A

Source: Official Guide

[deloitte247]

$$\frac{\left(x^4\cdot y^2-x^2\cdot y^2\right)}{x^3\cdot y^2}$$
$$\frac{x^2y^2\left(x^2-1\right)}{x\left(x^2y^2\right)}$$
$$\frac{\left(x^2-1\right)}{x}$$

Statement 1 is SUFFICIENT.

Statement 2
y=8

The value of y is useless as it has no place in the expression evaluated from the question stem, hence statement 2 is NOT SUFFICIENT.

Since Only statement 1 is SUFFICIENT. $$Option\ A\ is\ Correct.$$