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If x and y are integers such that (xy)^2 + x^2 – 2xy – 2

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by Max@Math Revolution » Tue Jul 24, 2018 11:32 pm

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A

B

C

D

E

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[Math Revolution GMAT math practice question]

If x and y are integers such that (xy)^2 + x^2 - 2xy - 2x + 2 = 0, what is the value of y?

A. -2
B. -1
C. 0
D. 1
E. 2
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by GMATGuruNY » Wed Jul 25, 2018 2:41 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x and y are integers such that (xy)^2 + x^2 - 2xy - 2x + 2 = 0, what is the value of y?

A. -2
B. -1
C. 0
D. 1
E. 2
We can PLUG IN THE ANSWERS, which represent the value of y.

B: y=-1
Substituting y=-1 into (xy)² + x² - 2xy - 2x + 2 = 0, we get:
x² + x² + 2x - 2x + 2 = 0
2x² + 2 = 0
x² + 1 = 0
x² = -1
Since the square of a value cannot be negative, eliminate B.

D: y=1
Substituting y=1 into (xy)² + x² - 2xy - 2x + 2 = 0, we get:
x² + x² - 2x - 2x + 2 = 0
2x² - 4x + 2 = 0
x² - 2x + 1 = 0
(x-1)² = 0
x = 1
Success!

The correct answer is D.
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by Jeff@TargetTestPrep » Thu Jul 26, 2018 3:26 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If x and y are integers such that (xy)^2 + x^2 - 2xy - 2x + 2 = 0, what is the value of y?

A. -2
B. -1
C. 0
D. 1
E. 2
(xy)^2 + x^2 - 2xy - 2x + 2 = 0

(xy)^2 - 2xy + 1 + x^2 - 2x + 1 = 0

(xy - 1)^2 + (x - 1)^2 = 0

If the sum of two squares is 0, each square must be 0 also.

(xy - 1)^2 = 0

xy - 1 = 0

xy = 1

and

(x - 1)^2 = 0

x - 1 = 0

x = 1

Since x = 1 and xy = 1, y must be 1 also.

Answer: D

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by Max@Math Revolution » Thu Jul 26, 2018 11:40 pm
=>

(xy)^2 + x^2 - 2xy - 2x + 2 = 0
=> (xy)^2 - 2xy + 1 + x^2 - 2x + 1 = 0
=> (xy - 1)^2 + (x - 1)2 = 0
=> xy = 1 and x = 1.
Thus , x = 1 and y = 1.

Therefore, the answer is D.
Answer: D
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