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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, 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, 21:41

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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Preparation for final battel: GMAT PREP-1 750 Q50 V41 - Oct 16 2011 GMAT PREP-2 710 Q50 V36 - Oct 22 2011 ==> Scored 50 in Quant second time in a row MGMAT---- -1 560 Q28 V39 - Oct 29 2011 ==> Left Quant half done and continued with Verbal. Happy to see Q39

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