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|a|=|b|, which of the following must be true : [#permalink]
 28 Oct 2012, 12:06
Question Stats:
58% (01:28) correct
41% (00:20) wrong based on 7 sessions
|a|=|b|, which of the following must be true : I. a=b II. |a|=-b III. -a=-b A. I only B. II only. C. III only. D. I and III only. E. None
Last edited by Bunuel on 29 Oct 2012, 00:58, edited 1 time in total.
Renamed the topic and edited the question.
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E
Let's say l a l = 1 and l b l = 1
For l a l = 1 ; a can be 1 or -1
Similarly b can be 1 or -1
This reasoning is used to get the answer
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himanshuhpr wrote: |a|=|b| , which of the following must be true :
1. a=b 2.|a|=-b 3.-a=-b
a. 1 only b. 2 only. C. 3 only. D. 1 and 3 only. E.none Responding to a pm: Neither method needs to be used here. Just think of the definition of mod we use to remove the mod sign. |x| = x if x >= 0 and |x| = -x if x < 0 We don't know whether a and b are positive or negative. |a|=|b| when absolute values of both a and b are the same. The signs can be different or same. There are 4 cases: a and b are positive, a is positive b is negative, a is negative b is positive, a and b are negative. For a must be true question, the relation should hold in every case. 1. a=b Doesn't hold when a and b have opposite signs. e.g. a = 5, b= -5 2.|a|=-b Doesn't hold when b is positive because -b will become negative while left hand side is always non negative. e.g. a = 5, b = 5 |5| \neq -5 3.-a=-b Doesn't hold when a and b have opposite signs. e.g. a = 5, b = -5 -5 \neq 5 Answer (E)
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VeritasPrepKarishma wrote: himanshuhpr wrote: |a|=|b| , which of the following must be true :
1. a=b 2.|a|=-b 3.-a=-b
a. 1 only b. 2 only. C. 3 only. D. 1 and 3 only. E.none Responding to a pm: Neither method needs to be used here. Just think of the definition of mod we use to remove the mod sign. |x| = x if x >= 0 and |x| = -x if x < 0 We don't know whether a and b are positive or negative. |a|=|b| when absolute values of both a and b are the same. The signs can be different or same. There are 4 cases: a and b are positive, a is positive b is negative, a is negative b is positive, a and b are negative. For a must be true question, the relation should hold in every case.
1. a=b Doesn't hold when a and b have opposite signs. e.g. a = 5, b= -5 2.|a|=-b Doesn't hold when b is positive because -b will become negative while left hand side is always non negative. e.g. a = 5, b = 5 |5| \neq -5 3.-a=-b Doesn't hold when a and b have opposite signs. e.g. a = 5, b = -5 -5 \neq 5 Answer (E) ^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually. If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks
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himanshuhpr wrote: ^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually.
If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks What I mean is that if we say any statement 'must be true' then it must hold for all 4 cases i.e. both a and b are positive, a is positive b is negative, a is negative b is positive and a and b are negative. i.e. if statement 1 i.e. a = b must be true, then it should be true in all 4 cases.
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VeritasPrepKarishma wrote: himanshuhpr wrote: ^^ by the highlighted statement above you mean that all the four cases you listed out should hold true for every stmt. 1. 2. 3. individually.
If yes then the only possible solution the to the question would be |a|=|b| , pl. re confirm ... thanks What I mean is that if we say any statement 'must be true' then it must hold for all 4 cases i.e. both a and b are positive, a is positive b is negative, a is negative b is positive and a and b are negative. i.e. if statement 1 i.e. a = b must be true, then it should be true in all 4 cases. Ok. thanks very much for the clarification... your blogs and posts are very informative 
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Thanks for the explanation.
Had a query on this one. Suppose if numbers weren't chosen to evaluate this.
Consider: |a|= |b|
this can be evaluated as: a,b have same signs or a,b have opposite signs
thus, a =b (same signs) and (a = -b or -a = b) for opposite signs.
|a| = -b would have two cases: a +ve , a -ve
thus, a = -b or -a = -b => a = b.
Thus, a = -b or -a=b AND a = b. which is what |a| = |b| boils down to.
Please help me understand if I'm missing anything.
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prep wrote: Thanks for the explanation.
Had a query on this one. Suppose if numbers weren't chosen to evaluate this.
Consider: |a|= |b|
this can be evaluated as: a,b have same signs or a,b have opposite signs
thus, a =b (same signs) and (a = -b or -a = b) for opposite signs.
|a| = -b would have two cases: a +ve , a -ve
thus, a = -b or -a = -b => a = b.
Thus, a = -b or -a=b AND a = b. which is what |a| = |b| boils down to.
Please help me understand if I'm missing anything. |a|= |b| basically means that the distance between a and zero on the number line is the same as the distance between b and zero on the number line. Thus either a=b (notice that it's the same as -a=-b) or a=-b (notice that it's the same as -a=b). Hope it helps.
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Re: |a|=|b|, which of the following must be true : [#permalink]
05 Dec 2012, 01:52
|a|=|b|
The equation doesn't tell us anything about the sign of a and b. All we know is that their absolute values are equal.
Possibilities:
|-5| = |5|
|5| = |5|
|5| = |-5|
I. a=b ==> When a=5 and b=-5, this is false!
II. |a|=-b ==> When a=-5 and b=5, this is false!
III. -a=-b ==> When a=-5 and b=5, this is false!
Answer: NONE or E
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Re: |a|=|b|, which of the following must be true :
[#permalink]
05 Dec 2012, 01:52
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