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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 \(-5 \neq 5\)

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

^^ 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. _________________

^^ 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

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 \(-a=b\)).

Re: |a|=|b|, which of the following must be true : [#permalink]
04 Jul 2013, 17:33

himanshuhpr wrote:

|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

Replace mod with its equivalent

We have one of these 4 equivalents for |a|=|b|:

-(a) = -(b) -(a) = b a = -(b) a=b

In the answer choices we can see that,

(i) is not the only possibility because we see there are other possibilities as seen above (ii) is equivalent to -(a) = -b or a = -b. Again these are not the only possibilities as we see there are other possibilities as seen above (iii) again is not the only possibility as there are other possibilities as seen above

Re: |a|=|b|, which of the following must be true : [#permalink]
16 Sep 2014, 19:44

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