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What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0

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What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 16 Feb 2017, 11:05
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What is the value of x?

(1) X^2 – x^2 = 0
(2) x/y + y/x = 0

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What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post Updated on: 08 Jun 2017, 13:58
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duahsolo wrote:
What is the value of x?

(1) x² – x² = 0
(2) x/y + y/x = 0


Awesome question!
Target question: What is the value of x?

Statement 1: x² – x² = 0
This means that x² = x²
As you might imagine, there are several solutions to this equation (in fact, the equation holds true for ANY value of x.
So, x = 0, x = 2, x = -3 (etc) are all solutions to the equation x² - x² = 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/y + y/x = 0
Subtract y/x from both sides to get: x/y = -y/x
Cross multiply to get: x² = -(y²)
This equation should be somewhat perplexing.
We know that y² must be greater than or equal to zero.
So, this means that -(y²) must be less than or equal to zero.
Likewise, x² must be greater than or equal to zero.

So, if x² = -(y²), then we are saying: A number that's greater than or equal to zero = -(y²) A number that's less than or equal to zero.
This equation holds true ONLY IF x = 0 and y = 0
So, we can conclude that x = 0
EDIT......
STOP!!
I have since been reminded that x = 0 and y = 0 does not satisfy the statement 2 equation x/y + y/x = 0, since 0/0 is undefined.

So, it seems, we have a faulty question.

Cheers,
Brent
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Originally posted by GMATPrepNow on 16 Feb 2017, 11:20.
Last edited by GMATPrepNow on 08 Jun 2017, 13:58, edited 1 time in total.
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 16 Feb 2017, 11:22
1
Option a. Insufficient. X can be any number
Option b.
X/y + y/x =0
(x^2+y^2)/xy=0
X^2+y^2=0
Since
X^2 and y^2 can't be negative. Both must be zero to fulfill the condition.
So x=0

Ans. Option B

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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 21 Feb 2017, 03:06
(1) Insufficient, as long as subject condition is applicable for all values of x
(2) x/y+y/x=0
x/y=-y/x
squaring
x^2/y^2=y^2/x^2
x^4=y^4
x^4-y^4=0
(x^2-y^2)(x^2+y^2)=0
So, both these conditions can exist only if x=y=0 Sufficient.
GMATPrepNow
Would you please advise if my reasoning is correct
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 21 Feb 2017, 03:07
(1) Insufficient, as long as subject condition is applicable for all values of x
(2) x/y+y/x=0
x/y=-y/x
squaring
x^2/y^2=y^2/x^2
x^4=y^4
x^4-y^4=0
(x^2-y^2)(x^2+y^2)=0
So, both these conditions can exist only if x=y=0 Sufficient.
GMATPrepNow
Would you please advise if my reasoning is correct
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 21 Feb 2017, 04:36
Top Contributor
Alexey1989x wrote:
(1) Insufficient, as long as subject condition is applicable for all values of x
(2) x/y+y/x=0
x/y=-y/x
squaring
x^2/y^2=y^2/x^2
x^4=y^4
x^4-y^4=0
(x^2-y^2)(x^2+y^2)=0
So, both these conditions can exist only if x=y=0 Sufficient.
GMATPrepNow
Would you please advise if my reasoning is correct


Squaring both sides of an equation (as you did at the beginning of your solution) can yield unintended consequences.
For example, consider the equation x = -x
This equation has only one solution: x = 0

However, if we take the equation x = -x and square both sides, we get: x² = (-x)²
This simplifies to be x² = x²
This new equation has infinitely many solutions. In fact, the new equation (x² = x²) holds true for ANY value of x.


The unintended consequences in your solution becomes apparent when you get to x^4=y^4 in your solution.
Notice that, with this new equation (x^4=y^4), we also have infinitely many solutions, including:
x = 1 and y = 1
x = 2 and y = 2
x = 2 and y = -2
x = -5 and y = 5
etc.

However, if you plug any of these solutions back into the original equation (x/y + y/x = 0), you'll find that they do not satisfy that equation.

Cheers,
Brent
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 06 Jun 2017, 01:03
#GMATPrepNow

I'm missing something. Since in the GMAT, all results of an equation must be for defined values of the variable, how can x = 0 in statement 2 and provide a unique solution? In the statement, if x=0, then y/x is undefined (division by 0).
Please advise.
Thanks a lot.
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 07 Jun 2017, 07:57
I agree with Mike2805 if x = 0 then y/x is undefined in B so this will not hold.
Answer should be E
Hi Bunuel , VeritasPrepKarishma , Can you please help in understanding the OA?
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 07 Jun 2017, 09:50
Imo B
From statement 1 we have x^2 =x^2 so it can take any value.
From statement 2
x^2=-y^2
There is only one value that satisfy this equation that is 0


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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 08 Jun 2017, 11:05
Also, nowhere it is written that x is a real number.

incase x=1i
and y=1
first equation stands
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 08 Jun 2017, 13:58
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Mike2805 wrote:
#GMATPrepNow

I'm missing something. Since in the GMAT, all results of an equation must be for defined values of the variable, how can x = 0 in statement 2 and provide a unique solution? In the statement, if x=0, then y/x is undefined (division by 0).
Please advise.
Thanks a lot.


Arghh! It was such a nice question too.
You're right, I neglect to remember that statement 2 says that x/y + y/x = 0
If x = 0 and y = 0, then we cannot say that x/y + y/x = 0, since 0/0 is undefined.

Unfortunately, the question is faulty :(

I have edited my response accordingly.

Cheers,
Brent
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 08 Jun 2017, 14:00
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ankursethi297 wrote:
Also, nowhere it is written that x is a real number.


All numbers that appear on the GMAT are real numbers.
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 16 Jul 2017, 13:13
What is the value of x?

(1) \(x^2 – x^2 = 0\)

x in this case can take any value, x can be = 1, or 2 or 3 or 4 or any other number

Hence, (1) ===== is NOT SUFFICIENT

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

\(x^2 + y^2 = 0\)

This is only possible when x and y are both ZERO.

So, \(x = 0\)

Hence, (2) ===== is SUFFICIENT

Hence, Answer is B

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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 27 Nov 2018, 08:15
duahsolo wrote:
What is the value of x?

(1) X^2 – x^2 = 0
(2) x/y + y/x = 0


So is it E or not? Can x be 0 or not?
Somebody explain it already please...
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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New post 27 Nov 2018, 21:34
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RK007 wrote:
duahsolo wrote:
What is the value of x?

(1) X^2 – x^2 = 0
(2) x/y + y/x = 0


So is it E or not? Can x be 0 or not?
Somebody explain it already please...



Hello

As it has already been discussed in this thread before, this is a faulty question. Thats because for second statement to be satisfied, the only solution is both x=y =0. And we cannot do 0/0.

So I suggest you ignore this question in particular, there are thousands of other good and brilliant questions to analyse. But this question also gives us a learning: division by 0 is not permitted.
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Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0 &nbs [#permalink] 27 Nov 2018, 21:34
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