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# a^2-b^2=b^2-c^2 . Is a = |b| ? (1) b= |c| (2) b= |a| Regards

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a^2-b^2=b^2-c^2 . Is a = |b| ? (1) b= |c| (2) b= |a| Regards [#permalink]

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12 Nov 2008, 15:30
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$$a^2-b^2=b^2-c^2$$. Is $$a = |b|$$?

(1) b= |c|

(2) b= |a|

Regards

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Director
Joined: 10 Sep 2007
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Re: DS: Try this one [#permalink]

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12 Nov 2008, 15:41
Statement 1: Tells us a^2 - b^2 = 0 because b = |c| => either b = c or b = -c which means (b+c)*(b-c) = 0. This statement also tells us that b is a positive number.
Now either a = b in which case a = |b| or a = -b in which case a is not equal to |b|.

Statement 2: Tells us b^2 - c^2 = 0 because b = |a| => either b = a or b = -a which means (a+b)*(a-b) = 0. This statement also tells us that b is a positive number.
Again either a = b in which case a = |b| or a = -b in which case a is not equal to |b|.

Even combining both is not going to yield any result.

So IMO E.

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SVP
Joined: 29 Aug 2007
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Re: DS: Try this one [#permalink]

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12 Nov 2008, 21:23
tarek99 wrote:
$$a^2-b^2=b^2-c^2$$. Is $$a = |b|$$?

(1) b= |c|
(2) b= |a|

E: $$a^2 - b^2 = b^2 - c^2$$

(1) when b = |c|, b is +ve, but c? do not know. c could be +ve or -ve. nsf.
(2) when b= |a|, b is +ve, but a? do not know. a could be +ve or -ve. nsf.

togather: still remains uncertainty that a could be -ve or +ve.
_________________

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SVP
Joined: 17 Jun 2008
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Re: DS: Try this one [#permalink]

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13 Nov 2008, 02:56
From stmt1: b = |c| or, b^2 = c^2 and hence, a^2 = b^2 or |a| = |b|...insufficient.

From stmt2: b = |a| or b^2 = a^2 or, |b| = |a|....insufficient.

E.

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Senior Manager
Joined: 21 Apr 2008
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Location: Motortown
Re: DS: Try this one [#permalink]

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13 Nov 2008, 11:28
E it is

stmt1: b^2 = c^2 -> |a| = |b| - InSuff
stmt2: b^2 = a^2 -> |a| = |b| - InSuff

Together InSuff

Good one tarek99

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SVP
Joined: 21 Jul 2006
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Re: DS: Try this one [#permalink]

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14 Nov 2008, 02:42
OA is E, but I don't quite understand what the question wants us to do. For example, it asks whether a=|b|, does that mean it's asking whether $$b^2=c^2$$? you see, if $$a^2=b^2$$, then our given equation $$a^2-b^2=b^2-c^2$$ will simply turn into $$0= b^2-c^2$$, therefore $$b^2=c^2$$.

is that how i'm suppose to look at it? If i'm wrong, would someone please show me how i'm suppose to look at this problem?
thanks

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Manager
Joined: 30 Sep 2008
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Re: DS: Try this one [#permalink]

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14 Nov 2008, 04:32
tarek99 wrote:
OA is E, but I don't quite understand what the question wants us to do. For example, it asks whether a=|b|, does that mean it's asking whether $$b^2=c^2$$? you see, if $$a^2=b^2$$, then our given equation $$a^2-b^2=b^2-c^2$$ will simply turn into $$0= b^2-c^2$$, therefore $$b^2=c^2$$.

is that how i'm suppose to look at it? If i'm wrong, would someone please show me how i'm suppose to look at this problem?
thanks

That means it's asking whether a > 0

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VP
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Re: DS: Try this one [#permalink]

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15 Nov 2008, 16:46
Q is asking is a = |b| square on both sides a^2 -b^2 =0??

Is that what the Q is asking for or not??

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Intern
Joined: 13 Oct 2008
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Re: DS: Try this one [#permalink]

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15 Nov 2008, 18:03
icandy wrote:
Q is asking is a = |b| square on both sides a^2 -b^2 =0??

Is that what the Q is asking for or not??

No because a^2-b^2=0 could result in a<0, this doesn't fit with a=|b|>=0

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Re: DS: Try this one   [#permalink] 15 Nov 2008, 18:03
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