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

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11 00:00

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

_________________
Current Student P
Joined: 18 Aug 2016
Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: If x ≠ 0, what is the value of x?  [#permalink]

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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
Manager  G
Joined: 27 Jan 2016
Posts: 123
Schools: ISB '18
GMAT 1: 700 Q50 V34 Re: If x ≠ 0, what is the value of x?  [#permalink]

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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
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If x ≠ 0, what is the value of x?  [#permalink]

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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.
Current Student P
Joined: 18 Aug 2016
Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 If x ≠ 0, what is the value of x?  [#permalink]

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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
Manager  B
Joined: 07 Jun 2017
Posts: 100
Re: If x ≠ 0, what is the value of x?  [#permalink]

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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.. ?
Current Student P
Joined: 18 Aug 2016
Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: If x ≠ 0, what is the value of x?  [#permalink]

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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
_________________
We must try to achieve the best within us

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

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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

_________________
Manager  S
Joined: 24 Nov 2018
Posts: 107
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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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.
Director  D
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If x ≠ 0, what is the value of x?  [#permalink]

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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

Intern  B
Joined: 28 Aug 2018
Posts: 27
Location: India
Schools: LBS '21 (A)
GMAT 1: 650 Q49 V31 GPA: 3.16
Re: If x ≠ 0, what is the value of x?  [#permalink]

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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.
Intern  B
Joined: 24 Jun 2017
Posts: 29
If x ≠ 0, what is the value of x?  [#permalink]

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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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