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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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Manager
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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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16 Feb 2017, 11:05
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Difficulty:

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Question Stats:

46% (01:07) correct 54% (01:18) wrong based on 167 sessions

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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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Updated on: 08 Jun 2017, 13:58
2
Top Contributor
1
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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Joined: 03 Jan 2017
Posts: 30
Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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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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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
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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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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
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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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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

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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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).
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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07 Jun 2017, 07:57
I agree with Mike2805 if x = 0 then y/x is undefined in B so this will not hold.
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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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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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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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Joined: 11 Sep 2015
Posts: 3237
Re: What is the value of x? (1) X^2 – x^2 = 0 (2) x/y + y/x = 0  [#permalink]

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08 Jun 2017, 13:58
Top Contributor
1
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).
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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08 Jun 2017, 14:00
Top Contributor
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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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

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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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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?
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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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27 Nov 2018, 21:34
1
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?

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.
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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