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GMAT - Problem Solving - Algebra

If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?

If xy not equal 0 and x2*y2 -xy = 6, which of the following could be y in terms of x?

I. 1/2x
II. -2/x
III. 3/x

Given:

x2y2 - xy = 6

assume xy = p

we can write the equation as

p2 - p = 6

p2 - p - 6 = 0

p2 - 3p + 2p - 6 = 0

p(p - 3) + 2 (p - 3) = 0

(p - 3) (p + 2) = 0

p = 3 or p = -2

xy = 3 or xy = -2

y = 3/x or y = -2/x

II and III

Given:

x2y2 - xy = 6

assume xy = p

we can write the equation as

p2 - p = 6

p2 - p - 6 = 0

p2 - 3p + 2p - 6 = 0

p(p - 3) + 2 (p - 3) = 0

(p - 3) (p + 2) = 0

p = 3 or p = -2

xy = 3 or xy = -2

y = 3/x or y = -2/x

II and III