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What is the value of |x| ? [#permalink]
 07 Oct 2011, 23:39
Question Stats:
57% (01:18) correct
42% (00:23) wrong based on 0 sessions
What is the value of |x| ? (1) x = -|x|(2) x^2 = 4
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Re: What is the value of |x| ? [#permalink]
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]
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]
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]
08 Oct 2011, 01:10
blink005 wrote: 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]
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]
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]
08 Oct 2011, 11:01
@fluke - crisp explanation. thx.
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Re: What is the value of |x| ? [#permalink]
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]
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]
08 Oct 2011, 22:03
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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]
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]
09 Oct 2011, 10:01
38 Secs to figure its B :D
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Re: What is the value of |x| ? [#permalink]
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]
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. So answer is B.
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Re: What is the value of |x| ? [#permalink]
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
Answer is B.
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Re: What is the value of |x| ? [#permalink]
12 Oct 2011, 11:41
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Re: What is the value of |x| ? [#permalink]
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]
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
Answer is B. 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]
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?
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Re: What is the value of |x| ?
[#permalink]
24 Oct 2011, 06:39
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