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a^2 - b^2 = b^2 - c^2 . Is a = |b| ? 1. b = |c| 2. b = |a| *

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VP
Joined: 05 Jul 2008
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a^2 - b^2 = b^2 - c^2 . Is a = |b| ? 1. b = |c| 2. b = |a| * [#permalink]

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09 May 2009, 10:29
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$$a^2 - b^2 = b^2 - c^2$$ . Is $$a = |b|$$ ?

1. $$b = |c|$$
2. $$b = |a|$$

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

What is the difference between a=|b|, |a|=b and |a|=|b|? I can see that a is +ve in one case and b is +ve in other, but if we square to get rid of the modulus operator all of them are the same right?
VP
Joined: 05 Jul 2008
Posts: 1401

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09 May 2009, 14:58
No It is not C try again.

When ever I see modulus, I tend to do two things

(1) get rid of the modulus by squaring on both sides

(2) consider all cases.

When to do (1) and when to do (2)? Any ideas

Here is what I did and got it wrong

a^2 - b^2 = b^2 - c^2 . Is a = |b| ?

1. b = |c|
2. b = |a|

Q is asking Is a = |b| ? ie a^2=b^2 (Do you guys agree?)

(0) a^2 - b^2 = b^2 - c^2

(1) b = |c| ie b ^2 = c^2

Substitute 1 in (0) , (0) becomes a^2=b^2

In 2 it is given that b=|a|, if i square it off it is b^2=a^2

Apparently I arrived at D and it is not the answer.

So I am wondering when to square and when to consider the +ve and _ve of the absolute value.
Senior Manager
Joined: 08 Jan 2009
Posts: 324

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10 May 2009, 00:23
i also go along with E.

Q is asking Is a = |b| ? ie a^2=b^2 (Do you guys agree?). No.
You know clearly that a^2=b^2 a can be +b or -b.
CEO
Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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10 May 2009, 06:08
a^2 - b^2 = b^2 - c^2 .

1. b = |c|
2. b = |a|

Look at these expressions carefully. They are not sensitive to substitution a for -a. And if a = |b|, a can be also a=-|b|
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SVP
Joined: 29 Aug 2007
Posts: 2467

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10 May 2009, 08:31
icandy wrote:
What is the difference between a=|b|, |a|=b and |a|=|b|? I can see that a is +ve in one case and b is +ve in other, but if we square to get rid of the modulus operator all of them are the same right?

1. If a = |b|, a is +ve but b could be +ve or -ve.
2. If b = |a|, b is +ve but a could be +ve or -ve.
3. If |b| = |b|, a and b could be +ve or -ve.

icandy wrote:
$$a^2 - b^2 = b^2 - c^2$$ . Is $$a = |b|$$ ?

1. $$b = |c|$$

2. $$b = |a|$$

$$a^2 - b^2 = b^2 - c^2$$
$$a^2 +c^2 = 2b^2$$

The basic question: is "a" +ve?

1. $$b = |c|$$
$$b^2 = c^2$$

$$a^2 + c^2 = 2b^2$$
$$a^2 + b^2 = 2b^2$$
$$a^2 = b^2$$
$$|a|=|b|$$
Since b is +ve, $$b = |a|$$ .........nsf...

2. $$b = |a|$$
Its the same as avove in 1. So nsf again ....

Togather: They both are same. So nsf...
E.
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SVP
Joined: 29 Aug 2007
Posts: 2467

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10 May 2009, 08:39
walker wrote:
And if a = |b|, a can be also a=-|b|

How is that possible?
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Joined: 17 Nov 2007
Posts: 3583
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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10 May 2009, 09:51
GMAT TIGER wrote:
walker wrote:
And if a = |b|, a can be also a=-|b|

How is that possible?

a^2 - b^2 = b^2 - c^2 .

1. b = |c|
2. b = |a|

values of a^2 and |a| is not sensitive to sign of a. So, if positive a is a solution, -a is also solution. In our case if a=|b| is a solution, a=-|b| is also solution and answer is E
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Joined: 17 Jun 2008
Posts: 1529

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17 May 2009, 22:51
First of all, if a^2 = b^2, then this means |a| = |b| and not a = |b| or b = |a|.

With this, stmt1 tells that b^2 = c^2. Hence, from the original equation, a^2 = b^2 and hence |a| = |b|.

Now, if I combine the second stmt, then,
b = |b|. That means, b is positive. But, this still does not tell whether a is +ve or -ve.

Re: a=|b|??   [#permalink] 17 May 2009, 22:51
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