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# What is the value of |x| ?

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Senior Manager
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What is the value of |x| ?  [#permalink]

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07 Oct 2011, 23:39
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What is the value of $$|x|$$ ?
(1) $$x = -|x|$$
(2) $$x^2 = 4$$

Official Guide 12 Question

 Question: 1 Page: 273 Difficulty: 600

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

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07 Oct 2011, 23:44
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

Its B

st1: X= -|X|
It tells us that X is negative . Nothing about the value of X.. hence insufficient

St2: X^2 = 4 this can be writen as |x|= 2
hence sufficient .
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 00:43
sudhir18n wrote:
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

Its B

st1: X= -|X|
It tells us that X is negative . Nothing about the value of X.. hence insufficient

St2: X^2 = 4 this can be writen as |x|= 2
hence sufficient .

Hi Sudhir,

For st1

When its given x = -|X|

does that mean we need to transfer the negative sign on the other side since we need to find what |x| is ? -x = |x| ?

but |x| is positive or 0 , right? so |x| = 0 / +ve ---- hence insufficient ? is this correct?
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 01:07
siddhans wrote:

Hi Sudhir,

For st1

When its given x = -|X|

does that mean we need to transfer the negative sign on the other side since we need to find what |x| is ? -x = |x| ?

but |x| is positive or 0 , right? so |x| = 0 / +ve ---- hence insufficient ? is this correct?

Statement 1 just means that x is negative.
e.g. |x|=5 & x=-|x|=>x=-5
|x|=10000 & x=-|x|=>x=-10000
We can't determine the value of x or |x|

So, yes what you said is corrected.
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 01:10
siddhans wrote:

Hi Sudhir,

For st1

When its given x = -|X|

does that mean we need to transfer the negative sign on the other side since we need to find what |x| is ? -x = |x| ?

but |x| is positive or 0 , right? so |x| = 0 / +ve ---- hence insufficient ? is this correct?

Statement 1 just means that x is negative.
e.g. |x|=5 & x=-|x|=>x=-5
|x|=10000 & x=-|x|=>x=-10000
We can't determine the value of x or |x|

So, yes what you said is corrected.

why are we finding value of x? we are asked to find |x|...i am not sure why did you find x in the examples above.???
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 01:15
My point was to tell you that statement 1 is insufficient.
I just tried to highlight different values of x and their relations.
Nothing else.
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 01:18
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

It is not mandatory to solve it algebraically. I have seen modulus question can be solved using PIN quite well.

Here,
Say;
x=0; |x|=0; -|x|=0; x=-|x|; So, x can be 0.
x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=2; |x|=2; -|x|=-2; x<>-|x|; So, x can't be 2.
We see that the modulus of a +ve number is always +ve. When we flip the sign of it we get a -ve. Thus, x can't be +ve because a +ve will not be equal to -ve.

x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.
x=-3; |x|=|-3|=3; -|x|=-3; So, x=-|x|; x can be 3.
In fact x can be any -ve number.

x <= 0 AND |x| >= 0
Not Sufficient.

2) x^2=4
x=+-2
So,
|x|=|-2|=2
Or
|x|=|+2|=2

Either way,
|x|=2
Sufficient.

Ans: "B"
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 11:01
@fluke - crisp explanation. thx.
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 21:10
fluke wrote:
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

It is not mandatory to solve it algebraically. I have seen modulus question can be solved using PIN quite well.

Here,
Say;
x=0; |x|=0; -|x|=0; x=-|x|; So, x can be 0.
x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=2; |x|=2; -|x|=-2; x<>-|x|; So, x can't be 2.
We see that the modulus of a +ve number is always +ve. When we flip the sign of it we get a -ve. Thus, x can't be +ve because a +ve will not be equal to -ve.

x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.
x=-3; |x|=|-3|=3; -|x|=-3; So, x=-|x|; x can be 3.
In fact x can be any -ve number.

x <= 0 AND |x| >= 0
Not Sufficient.

2) x^2=4
x=+-2
So,
|x|=|-2|=2
Or
|x|=|+2|=2

Either way,
|x|=2
Sufficient.

Ans: "B"

Sorry but i am having a hard time understanding whats going on here and have got more confused...
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 21:13
fluke wrote:
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

It is not mandatory to solve it algebraically. I have seen modulus question can be solved using PIN quite well.

Here,
Say;
x=0; |x|=0; -|x|=0; x=-|x|; So, x can be 0.
x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=2; |x|=2; -|x|=-2; x<>-|x|; So, x can't be 2.
We see that the modulus of a +ve number is always +ve. When we flip the sign of it we get a -ve. Thus, x can't be +ve because a +ve will not be equal to -ve.

x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.
x=-3; |x|=|-3|=3; -|x|=-3; So, x=-|x|; x can be 3.
In fact x can be any -ve number.

x <= 0 AND |x| >= 0
Not Sufficient.

2) x^2=4
x=+-2
So,
|x|=|-2|=2
Or
|x|=|+2|=2

Either way,
|x|=2
Sufficient.

Ans: "B"

Sorry but i am having a hard time understanding whats going on here and have got more confused...

x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.

These 2 above statements confused me a lot...

if x=-2 ; whats the reason for doing this step |x| = |-2|? and then -|x| =-2 ??

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

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08 Oct 2011, 22:03
1
siddhans wrote:

What is the value of |x|?
(1) x = –|x|
(2) $$x^2$$ = 4

Sorry but i am having a hard time understanding whats going on here and have got more confused...

x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.

These 2 above statements confused me a lot...

if x=-2 ; whats the reason for doing this step |x| = |-2|? and then -|x| =-2 ??

What is modulus OR ||?

If a variable is -ve, and we wrap it around with ||, it becomes +ve.
If a variable is +ve, and we wrap it around with ||, it remains +ve.
If a variable is 0, and we wrap it around with ||, it remains 0.

So,
-2; Wrap it around; |-2|=2
+2; Wrap it around; |+2|=+2=2
0; Wrap it around; |0|=0

Statement 1:
(1) x = –|x|

Let's say x=1;
L.H.S.=x=1
R.H.S.=-|x|=-|1|=-1
We know; 1 <> -1, so the expression x=-|x| doesn't hold good for x=1; And it won't hold good for any +ve number.

Now, let's say x=-1;
L.H.S.=x=-1
R.H.S.=-|x|=-|-1|=-1
We know; -1 = -1, so the expression x=-|x| does indeed hold good for x=-1; And it will hold good for any -ve number.

For x=-0.464654 OR x=-100000; this expression will hold good. Thus, we won't be able to find a conclusive value for x.
Not Sufficient.
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Re: What is the value of |x| ?  [#permalink]

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08 Oct 2011, 22:41
fluke wrote:
siddhans wrote:

What is the value of |x|?
(1) x = –|x|
(2) $$x^2$$ = 4

Sorry but i am having a hard time understanding whats going on here and have got more confused...

x=1; |x|=1; -|x|=-1; x<>-|x|; So, x can't be 1.
x=-2; |x|=|-2|=2; -|x|=-2; So, x=-|x|; x can be 2.

These 2 above statements confused me a lot...

if x=-2 ; whats the reason for doing this step |x| = |-2|? and then -|x| =-2 ??

What is modulus OR ||?

If a variable is -ve, and we wrap it around with ||, it becomes +ve.
If a variable is +ve, and we wrap it around with ||, it remains +ve.
If a variable is 0, and we wrap it around with ||, it remains 0.

So,
-2; Wrap it around; |-2|=2
+2; Wrap it around; |+2|=+2=2
0; Wrap it around; |0|=0

Statement 1:
(1) x = –|x|

Let's say x=1;
L.H.S.=x=1
R.H.S.=-|x|=-|1|=-1
We know; 1 <> -1, so the expression x=-|x| doesn't hold good for x=1; And it won't hold good for any +ve number.

Now, let's say x=-1;
L.H.S.=x=-1
R.H.S.=-|x|=-|-1|=-1
We know; -1 = -1, so the expression x=-|x| does indeed hold good for x=-1; And it will hold good for any -ve number.

For x=-0.464654 OR x=-100000; this expression will hold good. Thus, we won't be able to find a conclusive value for x.
Not Sufficient.

Thats a great explnation!!!... I knew what modulus is but confused on the cases you had mentioned earlier... Do you know how can we do this algebrically too? Just curious to know
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Re: What is the value of |x| ?  [#permalink]

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09 Oct 2011, 10:01
38 Secs to figure its B :D
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Re: What is the value of |x| ?  [#permalink]

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10 Oct 2011, 06:08
Ans is B.
Question asks for the value of |x|

Statement 2) gives us +-2 and since we need the absolute value... therefore we can only get 2.
Sufficient
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Re: What is the value of |x| ?  [#permalink]

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11 Oct 2011, 04:29
siddhans wrote:
Searched for this multiple times before posting but couldnt find it...

What is the value of |x| ?
(1) x = –|x|
(2) $$x^2$$ = 4

Using statement 1 : We cannot find the value of x

Using statement two we know x= +- 2...so |x| is always 2. Hence sufficient.

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

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11 Oct 2011, 16:37
|x|=?

1. Not sufficient
x= -|x|

=> |x| = -x

without knowing x, we cannot saying anything about |x|.

all we know from the given expression that x is -ve

=> x can be -1 or -2..and they all have different |x| values.

2. Sufficient

x^2= 4

=> |x|=2

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

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12 Oct 2011, 11:41
B is the answer as |x| = 2.
St1 just tells us that x is -ve
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Re: What is the value of |x| ?  [#permalink]

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18 Oct 2011, 23:11
+B
fluke and others, just want to know if this question is really of 600 to 700 level ?
or sub 600 level ?
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Re: What is the value of |x| ?  [#permalink]

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24 Oct 2011, 02:17
Spidy001 wrote:
|x|=?

1. Not sufficient
x= -|x|

=> |x| = -x

without knowing x, we cannot saying anything about |x|.

all we know from the given expression that x is -ve

=> x can be -1 or -2..and they all have different |x| values.

2. Sufficient

x^2= 4

=> |x|=2

Can someone explain whats wrong with this method ?

1) x = -|x|

this x = - (-x) or x = - (+x)

since |x| can be +ve pr -ve

thus

x = x or x = -x

x - x = 0 or x + x = 0

0=0 or 2x = 0

x =0....
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Re: What is the value of |x| ?  [#permalink]

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24 Oct 2011, 06:39
siddhans wrote:
:(

Can someone explain whats wrong with this method ?

1) x = -|x|

this x = - (-x) or x = - (+x)

since |x| can be +ve pr -ve

thus

x = x or x = -x

x - x = 0 or x + x = 0

0=0 or 2x = 0

x =0....

|x| can't be negative. Absolute value of a number is always non-negative.

Do you follow?
Re: What is the value of |x| ?   [#permalink] 24 Oct 2011, 06:39

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