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Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 00:15
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. _________________
Hit kudos if my post helps you. You may send me a PM if you have any doubts about my solution or GMAT problems in general.
Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 00:18
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.
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Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 20:10
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...
Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 20:13
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 ??
Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 21:03
1
This post received KUDOS
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. _________________
Re: What is the value of |x| ? [#permalink]
08 Oct 2011, 21:41
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
Re: What is the value of |x| ? [#permalink]
09 Oct 2011, 09:01
38 Secs to figure its B :D _________________
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