Given that x > 0, y > 0, and (x^2)y = x, whic… | GMAT Sprint

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PS · Problem Solving

sub-505

Algebra

Given that $x > 0$ , $y > 0$ , and $(x^2)y = x$ , which of the following expressions MUST equal $x$ ?

Correct answer marked below

1/(y^2)

1/y

Correct

y

y^2

y^2 - 2y + 1

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Explanation

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Official Explanation

Official

Starting with the equation

(x^2)y = x

, subtract

x

from both sides to get

(x^2)y - x = 0

. Factor out

x

to obtain

x(xy - 1) = 0

.…

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What this question tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.