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What is the value of x?

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What is the value of x? [#permalink]

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25 Sep 2017, 23:56
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Question Stats:

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What is the value of x?

(1) x^2 – y^2 = 0

(2) x/y + y/x = 0
[Reveal] Spoiler: OA

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What is the value of x? [#permalink]

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26 Sep 2017, 00:11
Bunuel wrote:
What is the value of x?

(1) x^2 – y^2 = 0

(2) x/y + y/x = 0

Statement 1: $$(x-y)(x+y)=0$$, so either $$x-y=0$$ or $$x+y=0$$, in either case we have two variables and one equation. hence insufficient

Statement 2: Solve it to get $$\frac{(x^2+y^2)}{xy}=0$$

or $$x^2+y^2 = 0$$. Sum of two positive numbers is 0 only when both the numbers are 0

Hence $$x=0$$. Sufficient

Option B

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Re: What is the value of x? [#permalink]

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26 Sep 2017, 00:19
(1) x^2 – y^2 = 0
x^2 = y^2 , but this is not enough to answer
the question to what is the value of x(Insufficient)

(2) x/y + y/x = 0
This equation can be re-written as x^2 + y^2=0
This is only when possible when x=y=0 (Sufficient)(Option B)
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What is the value of x? [#permalink]

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15 Oct 2017, 16:18
niks18 wrote:
Bunuel wrote:
What is the value of x?

(1) x^2 – y^2 = 0

(2) x/y + y/x = 0

Statement 1: $$(x-y)(x+y)=0$$, so either $$x-y=0$$ or $$x+y=0$$, in either case we have two variables and one equation. hence insufficient

Statement 2: Solve it to get $$\frac{(x^2+y^2)}{xy}=0$$

or $$x^2+y^2 = 0$$. Sum of two positive numbers is 0 only when both the numbers are 0

Hence $$x=0$$. Sufficient

Option B

In order to make (2) works, both x, y have to be different from 0.
So, how can x = y = 0 ?
I don't think this is a valid solution.
Plz show the source of the question, thanks!

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Director
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Re: What is the value of x? [#permalink]

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17 Oct 2017, 11:06
elainetianfong wrote:
niks18 wrote:
Bunuel wrote:
What is the value of x?

(1) x^2 – y^2 = 0

(2) x/y + y/x = 0

Statement 1: $$(x-y)(x+y)=0$$, so either $$x-y=0$$ or $$x+y=0$$, in either case we have two variables and one equation. hence insufficient

Statement 2: Solve it to get $$\frac{(x^2+y^2)}{xy}=0$$

or $$x^2+y^2 = 0$$. Sum of two positive numbers is 0 only when both the numbers are 0

Hence $$x=0$$. Sufficient

Option B

In order to make (2) works, both x, y have to be different from 0.
So, how can x = y = 0 ?
I don't think this is a valid solution.
Plz show the source of the question, thanks!

Hi elainetianfong

For the source of the question, kindly consult owner of the question Bunuel

As far as the equation in statement 2 is concerned, in an equality if RHS is $$0$$, then LHS has to be $$0$$. Here the LHS is an algebraic expression that is not presented in its simplest form. We need to find the roots of this quadratic equation. Hence on simplification it yields $$x^2+y^2$$ which will yield $$x=y=0$$. In graphical terms it will be a DOT in the x-y plane at the origin.

Hi Bunuel - can you provide more technical clarity on this.

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Re: What is the value of x?   [#permalink] 17 Oct 2017, 11:06
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