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# If x ≠ 0, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 59586
If x ≠ 0, what is the value of x?  [#permalink]

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28 Aug 2017, 03:27
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Difficulty:

95% (hard)

Question Stats:

39% (02:17) correct 61% (02:08) wrong based on 165 sessions

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Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

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Re: If x ≠ 0, what is the value of x?  [#permalink]

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28 Aug 2017, 03:35
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

What is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

(1) x can take 0 or 1 or -1
in all the cases the distance between x and -x on the number line is equal to the distance between x^2 and -x^2
not sufficient

(2) if x = 0 then ? represents any one of the operations
if x=-1 then ? represents addition
if x=1 then ? represent subtraction
not sufficient

on combining also not sufficient
E
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Luckisnoexcuse
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Joined: 27 Jan 2016
Posts: 123
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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28 Aug 2017, 03:50
1
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

Stmnt 1) x = 1 or -1 . Insuff
if subtraction x=1
Hence E
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Joined: 07 Jun 2017
Posts: 100
Re: If x ≠ 0, what is the value of x?  [#permalink]

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29 Aug 2017, 02:53
1
For the first statement,
distance between x and -x is same as x^2 and -x^2
let say x=1, -1, distance is 2
and 1^2 and -1^2, distance is 2
(GMAT number property, -x^2= -1(x)^2 so -1^2= -1)
insuff.

For the second statement, x? |x| = 0, ? represent + / - / x < does that mean only represent one of them, or all three?
then x must be -ve? x-x= 0
I actually don't really understand the second statement.
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If x ≠ 0, what is the value of x?  [#permalink]

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29 Aug 2017, 02:56
pclawong wrote:
For the first statement,
distance between x and -x is same as x^2 and -x^2
let say x=1, -1, distance is 2
and 1^2 and -1^2, distance is 2
(GMAT number property, -x^2= -1(x)^2 so -1^2= -1)
insuff.

For the second statement, x? |x| = 0, ? represent + / - / x < does that mean only represent one of them, or all three?
then x must be -ve? x-x= 0
I actually don't really understand the second statement.

x? |x| = 0
? can represent any of the three (+, -, *) basis the value of x
if u consider x as 1 then ? is -
if u consider x as -1 then ? is +
if u consider x as 0 then ? can take any of -,+,*
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Luckisnoexcuse
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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29 Aug 2017, 03:03
Luckisnoexcuse wrote:
pclawong wrote:
For the first statement,
distance between x and -x is same as x^2 and -x^2
let say x=1, -1, distance is 2
and 1^2 and -1^2, distance is 2
(GMAT number property, -x^2= -1(x)^2 so -1^2= -1)
insuff.

For the second statement, x? |x| = 0, ? represent + / - / x < does that mean only represent one of them, or all three?
then x must be -ve? x-x= 0
I actually don't really understand the second statement.

x? |x| = 0
? can represent any of the three (+, -, *) basis the value of x
if u consider x as 1 then ? is -
if u consider x as -1 then ? is +
if u consider x as 0 then ? can take any of -,+,*

so, again, x can be 1 or x can be -1?
insuff.. ?
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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29 Aug 2017, 03:08
pclawong wrote:
Luckisnoexcuse wrote:
pclawong wrote:
For the first statement,
distance between x and -x is same as x^2 and -x^2
let say x=1, -1, distance is 2
and 1^2 and -1^2, distance is 2
(GMAT number property, -x^2= -1(x)^2 so -1^2= -1)
insuff.

For the second statement, x? |x| = 0, ? represent + / - / x < does that mean only represent one of them, or all three?
then x must be -ve? x-x= 0
I actually don't really understand the second statement.

x? |x| = 0
? can represent any of the three (+, -, *) basis the value of x
if u consider x as 1 then ? is -
if u consider x as -1 then ? is +
if u consider x as 0 then ? can take any of -,+,*

so, again, x can be 1 or x can be -1?
insuff.. ?

Correct and hence E
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Luckisnoexcuse
Math Expert
Joined: 02 Sep 2009
Posts: 59586
Re: If x ≠ 0, what is the value of x?  [#permalink]

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24 Dec 2018, 04:12
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

_________________
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Location: India
GPA: 3.27
WE: General Management (Retail Banking)
Re: If x ≠ 0, what is the value of x?  [#permalink]

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25 Dec 2018, 23:31
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

Statement 1) x can be 1 or -1. Since, the for x=1, and x=-1, the distance between x and -x on the number line is equal to the distance between x^2 and -x^2. Insufficient.

Statement 2) For addition, x+|X|=0, x=-1 or 0 but x ≠ 0, so x=-1, For subtraction, x-|x|=0, x=1. For multiplication, x*|x|=0, x= 0. SO, x can be 1 or -1. Insufficient.

(1)+(2),

x can be 1 or -1. Insufficient.

Option E is the correct answer.
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Re: If x ≠ 0, what is the value of x?  [#permalink]

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25 Dec 2018, 23:55
1
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

Given, x ≠ 0
DS Question : what is the value of x?

Statement (1): Since distance between x and -x on the number line is equal to the distance between x^2 and -x^2. Means x and x^2 must have same mod value.
This is possible only if x =1,-1,0. Since , x ≠ 0
So, x= 1,-1
NOT SUFFICIENT

Statement (2): x ? |x| = 0, where ? can be +, -, *
If ? = +
x+|x| = 0
x= -|x|
So, x<0

If ? = -
x-|x| = 0
x= |x|
So, x>0

If ? = *
x*|x| = 0
So, x=0
Since it is given that x ≠ 0.
So ?=* is not possible.

So overall either x<0 or x>0.
NOT SUFFICIENT

Combined statement :
x= -1,1
NOT SUFFICIENT

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Re: If x ≠ 0, what is the value of x?  [#permalink]

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28 Dec 2018, 07:54
Luckisnoexcuse wrote:
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

What is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

(1) x can take 0 or 1 or -1
in all the cases the distance between x and -x on the number line is equal to the distance between x^2 and -x^2
not sufficient

(2) if x = 0 then ? represents any one of the operations
if x=-1 then ? represents addition
if x=1 then ? represent subtraction
not sufficient

on combining also not sufficient
E

x cannot be equal to 0. It is mentioned in the question stem.
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Joined: 24 Jun 2017
Posts: 29
If x ≠ 0, what is the value of x?  [#permalink]

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26 May 2019, 13:41
shashankism wrote:
Bunuel wrote:

Fresh GMAT Club Tests' Challenge Question:

If x ≠ 0, what is the value of x?

(1) The distance between x and -x on the number line is equal to the distance between x^2 and -x^2

(2) x ? |x| = 0, where ? represents one of the three operations addition, subtraction, or multiplication

Given, x ≠ 0
DS Question : what is the value of x?

Statement (1): Since distance between x and -x on the number line is equal to the distance between x^2 and -x^2. Means x and x^2 must have same mod value.
This is possible only if x =1,-1,0. Since , x ≠ 0
So, x= 1,-1
NOT SUFFICIENT

Statement (2): x ? |x| = 0, where ? can be +, -, *
If ? = +
x+|x| = 0
x= -|x|
So, x<0

If ? = -
x-|x| = 0
x= |x|
So, x>0

If ? = *
x*|x| = 0
So, x=0
Since it is given that x ≠ 0.
So ?=* is not possible.

So overall either x<0 or x>0.
NOT SUFFICIENT

Combined statement :
x= -1,1
NOT SUFFICIENT

hi, but isn't it given that it represents only one of the operations out of the three so ( i assume here that not both by the language) , how do we conclude statement 2 , it can't be multiplication for sure , but it can EITHER be addition or subtraction not both as what i understand from the lang so if its add x<0 and combined with stat (1) x= -1 but if its sub x>0 and combined with stat 2 x=1 . so considering that it can be one of the three operations with stat (1) , i think we should get a definite answer .

please correct my thought process Bunuel chetan2u
If x ≠ 0, what is the value of x?   [#permalink] 26 May 2019, 13:41
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