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# Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y

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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
Statement 1:
(x,y)=(5,5) --> x²=xy
(x,y)=(-5,5) --> x²<>xy
not sufficient

Statement 2:
x=y --> xx=xy or x²=xy
sufficient

B
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
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I agree with bogos.

Stmt1:
x^2 - y^2 = (x+5)(x-5)
x^2 - y^2 = x^2 - 25
0 = y^2 - 25
y = +5, -5

plugin a possible value of y into the equation x^2 - y^2 = x^2 - 25
you can see when that y can be -5 and x can 5. But plugging in the same value into x^2 = xy would yield 25 = -25.
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
dobinnoli wrote:
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Is x(x-y)=0

So is x=0 or x=y?

Statement 1

Obviously x is not equal to y otherwise LHS and RHS should be zero

Is x = 0

Is -y^2 = -25, could be but we don't know

Statement 2

x=y, yes. This is correct and sufficient

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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
iliavko wrote:
Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here

I guess we are using 5 in order to make (x+y)(x-y) = 0, which is the easiest way to figure out the possible values of x
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
dobinnoli wrote:
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

PS21275

$$x^2 = xy$$?
$$x^2 - xy = 0$$?
$$x(x-y) = 0$$?
$$x = 0$$ or $$x = y$$?

(1) $$x^2 – y^2 = (x + 5)(y - 5)$$
$$(x+y)(x-y) = (x+5)(y-5)$$

if $$x = y = 5$$, then $$x^2 = xy$$
if $$x = -5$$, then $$x^2$$ is not equal to xy

INSUFFICIENT.

(2) Directly gives us our answer; SUFFICIENT.

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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
1
Kudos
x^2 - y^2 = (x+5)(x-5)
x^2 - y^2 = x^2 - 25
0 = y^2 - 25
y = +5, -5

plugin a possible value of y into the equation x^2 - y^2 = x^2 - 25
you can see when that y can be -5 and x can 5. But plugging in the same value into x^2 = xy would yield 25 = -25.

s2

x=y sufficient
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
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Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
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