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Re: What is the value of |x| ? [#permalink]
23 Jul 2012, 03:43
1
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Expert's post
4
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SOLUTION
What is the value of |x| ?
(1) x = - |x| --> \(|x|=-x\). This equation holds true for any \(x\) which is less than or equal to zero, so all we know from this statement is that \(x\leq{0}\). Not sufficient.
Re: What is the value of |x| ? [#permalink]
25 Jul 2012, 01:27
Please confirm if this is right logic to prove x<=0?
from condition 1: x=-|x|
thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0 and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x
Thus in combination x<=0.
cyberjadugar wrote:
Hi,
Difficulty level: 600
Using (1), x = -|x| or \(x \leq 0\), Insufficient.
Re: What is the value of |x| ? [#permalink]
27 Jul 2012, 06:31
Expert's post
SOLUTION
What is the value of |x| ?
(1) x = - |x| --> \(|x|=-x\). This equation holds true for any \(x\) which is less than or equal to zero, so all we know from this statement is that \(x\leq{0}\). Not sufficient.
Re: What is the value of |x| ? [#permalink]
29 Jul 2012, 05:58
Cyberjadugar/Bunuel, is Pavan puneets approach right to confirm stmt ( 1) leads us to x<=0 ? can you just break stmt 1 down for us a little please ?
pavanpuneet wrote:
Please confirm if this is right logic to prove x<=0?
from condition 1: x=-|x|
thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0 and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x
Thus in combination x<=0.
cyberjadugar wrote:
Hi,
Difficulty level: 600
Using (1), x = -|x| or \(x \leq 0\), Insufficient.
Re: What is the value of |x| ? [#permalink]
29 Jul 2012, 06:29
Expert's post
vinay911 wrote:
Cyberjadugar/Bunuel, is Pavan puneets approach right to confirm stmt ( 1) leads us to x<=0 ? can you just break stmt 1 down for us a little please ?
pavanpuneet wrote:
Please confirm if this is right logic to prove x<=0?
from condition 1: x=-|x|
thus, if x>0 ==> x=-x ==> 2x=0 ==> x=0 and if x<0 ==> x=-(-x) ==> x=x...however x<0, then for this condition x will be always less than zero to satisfy x=x
Thus in combination x<=0.
cyberjadugar wrote:
Hi,
Difficulty level: 600
Using (1), x = -|x| or \(x \leq 0\), Insufficient.
Using (2), \(x^2 = 4\) or |x| = 2. Sufficient.
Answer (B)
Regards,
From (1) we can conclude that \(x\leq{0}\) (check this: what-is-the-value-of-x-136195.html#p1108170), though the approach you are referring to is not precise enough. _________________
Re: What is the value of |x| ? [#permalink]
29 Jul 2012, 07:10
2
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pavanpuneet wrote:
Hi Bunuel, Can you please let me know where I have made the mistake to derive x<=0. It will be really helpful. Thanks.
Sure. If we do the way you are proposing then we should consider two cases:
If \(x\leq{0}\), then we would have that \(x=-(-x)\) --> \(x=x\), which is obviously true. So, \(x=-|x|\) holds true for any \(x\) which is \(\leq{0}\);
If \(x>{0}\), then we would have that \(x=-x\) --> \(2x=0\) --> \(x=0\), which is not a valid solution since we are considering the range when \(x>{0}\). So, if \(x>{0}\) then \(x=-|x|\) has no valid solutions.
Therefore, from the above we have that \(x=-|x|\) holds true only when \(x\leq{0}\).
Now, you could conclude that right away, since we can rewrite \(x=-|x|\) as \(|x|=-x\), which according to the properties of absolute value is true for \(x\leq{0}\).
Re: What is the value of |x| ? [#permalink]
17 Aug 2012, 05:01
I understand the answer explanation, so thanks to everyone who contributed. But what I'm confused is when they use the term "value." Does that always mean they are looking for a single number?
Re: What is the value of |x| ? [#permalink]
17 Aug 2012, 05:17
Expert's post
bpdulog wrote:
I understand the answer explanation, so thanks to everyone who contributed. But what I'm confused is when they use the term "value." Does that always mean they are looking for a single number?
When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.
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We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.
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Stmt 1: no value, stmt2: x = 2 or -2 and !x! = 2, so answer i stmt B alone
Re: DS question from OG [#permalink]
30 Dec 2013, 11:07
1
This post was BOOKMARKED
seabhi wrote:
1. What is the value of |x| ?
(1) x = –|x| (2) x2 = 4
Posting OG question, did not find in the search.
First off, this is a "value" DS question therefore in order to be sufficient, we must be able to calculate a specific value for x
S1: x could be a suite of numbers such as: any negative integer or fraction, and 0 --> not sufficient S2: 2x = 4 - therefore x = 2 --> sufficient because we know the value of x, and can now answer the question stem |x| --> |2| = 2
Re: What is the value of |x| ? [#permalink]
30 May 2014, 10:00
Hi,
I've got a big dilemma for this question.
For statement 2 x^2=4
I see 3 solution fitting: i) x=2 >> 2^2=4 therefore abs(2)=2
ii) x=(-2) >> (-2)^2=4 therefore abs(-2)=2
BUT iii) sx=qr(4) >>> sqr(4)^2=4. Am I not correct on this? The sterm/question does not say that x has to be an integer right? So sqr(4) can fit in here, isn't it? therefore abs(sqr(4))=sqr(4)
Therefore statement 2 is insufficient.
Between the OG and Online explanations, I do not understand why sqr(4) could not fit in statement 2.
Re: What is the value of |x| ? [#permalink]
30 May 2014, 10:04
1
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Expert's post
bdrrr wrote:
Hi,
I've got a big dilemma for this question.
For statement 2 x^2=4
I see 3 solution fitting: i) x=2 >> 2^2=4 therefore abs(2)=2
ii) x=(-2) >> (-2)^2=4 therefore abs(-2)=2
BUT iii) sx=qr(4) >>> sqr(4)^2=4. Am I not correct on this? The sterm/question does not say that x has to be an integer right? So sqr(4) can fit in here, isn't it? therefore abs(sqr(4))=sqr(4)
Therefore statement 2 is insufficient.
Between the OG and Online explanations, I do not understand why sqr(4) could not fit in statement 2.
Thx
\(\sqrt{4}=2\).
\(x^2=4\) means that \(x=\sqrt{4}=2\) or \(x=-\sqrt{4}=-2\). Two solutions. _________________
Re: What is the value of |x| ? [#permalink]
07 May 2015, 21:52
1
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Expert's post
1
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A few students above had difficulty in processing the first statement: x = -|x|
Here's how you can think through this statement visually:
|x| denotes the distance of an unknown number x from the zero point on the number line. Being the distance, |x| is always non-negative. (Please note that it will be wrong to say that the distance |x| is always positive, because the word 'positive' means 'strictly greater than zero'. It is possible that a point lies ON the zero point, thereby making its distance from the zero point equal to zero. )
So, x = (-)(a positive number) = (a negative number)
Or, x can be equal to zero (that is, on the number line, point x lies ON the point zero. Therefore, |x| = distance between 0 and x = 0 as well)
The important takeaway is that when processing equations of the type x = -|x| etc., start by first considering that |x| is non-negative, since it represents the distance of a number from the zero point on the number line.
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