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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sat Oct 31, 2020 7:01 am

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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

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 31, 2020 7:01 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

by deloitte247 » Sun Nov 08, 2020 4:48 am

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

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. $$Option\ A\ is\ Correct.$$

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