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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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Current Student
Joined: 11 May 2008
Posts: 551
a^2 - b^2 = b^2 - c^2 . Is a = |b| ? 1) b = |c| 2) b = |a| * [#permalink]

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29 Aug 2008, 00:48
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

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Director
Joined: 03 Sep 2006
Posts: 840
Re: HOW TO SOLVE THIS? [#permalink]

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29 Aug 2008, 00:59
(a+b)*(a-b) = (b+c)*(b-c)

From ( i ) b = c or b = -c

If b = c, then a = b or a = -b, which implies a = |b|

If b = -c, then a = b or a = -b, which implies a = |b|

Thus ( i ) is sufficient

From ( ii ) b = a or b = -a

also shows that a = |b|

Thus ( ii ) is sufficient

Thus answer should be "D"
Director
Joined: 23 Sep 2007
Posts: 761
Re: HOW TO SOLVE THIS? [#permalink]

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29 Aug 2008, 02:35
arjtryarjtry wrote:
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

Guessing E

not sure if I interpret what the question is asking correctly.

The question is asking if a is positive.

rearrange the stem to

a^2 + c^2 = b^2 + b^2

statement 1: b^2 = c^2 leads to a^2 = b^2
a could be positive or negative
insuff

statement 2: a^2 = b^2, it is the same as statement 1, so insuff

together, 2 statements are the same
insuff
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York
Re: HOW TO SOLVE THIS? [#permalink]

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29 Aug 2008, 07:42
arjtryarjtry wrote:
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

1) b = |c|
a^2 - b^2 =0 a=b or a=-b ( b is positive and a can be -ve or +ve)
Is a = |b| ? Yes or No
not suffcieint
2) b = |a| b= a or b=-a (a is -ve and b is positive)
Is a = |b| ? Yes or No
insuffcient

combine.
not suffcient
E
_________________

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Senior Manager
Joined: 09 Oct 2007
Posts: 456
Re: HOW TO SOLVE THIS? [#permalink]

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29 Aug 2008, 08:41
Rephrase the question as:

If |a| = |b| = |c|, is a positive?

1) b = |c|, thus b is positive. Nothing about a. INSUFF.
2) b = |a|, thus b is positive. Again, nothing about a. INSUFF
Clearly 1+2 taken together are also INSUFF.
Anwer: E for me.
VP
Joined: 21 Jul 2006
Posts: 1455
Re: HOW TO SOLVE THIS? [#permalink]

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30 Aug 2008, 04:34
arjtryarjtry wrote:
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

Interesting problem. If I take a look at this problem more abstractly, the question is asking whether a is positive or zero.

(1) b is zero or positive. So, if you take the absolute value of b from this restriction, a will be either positive or zero. True

(2) we don't know the actual sign of a, however, because b is either positive or zero, the absolute value of that will also be positive or a zero, so suff.

Damn, I really hate these kind of problems, but I believe that it should be D?

by the way, what is the abstract meaning behind $$a^2-b^2=b^2-c^2$$? This expression must be telling us something, but I can't seem to figure out what it is. For example, if we would have the expresion $$|x+y|<|x|+|y|$$, then you would know instantly that the signs for x and y are opposite from each other. So what is the expression from this problem trying to tell us without doing any math. There must be a message behind this expression.
VP
Joined: 17 Jun 2008
Posts: 1479
Re: HOW TO SOLVE THIS? [#permalink]

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30 Aug 2008, 14:08
I will go with C.

The question is really asking whether square of a is the same as that of b.

From stmt 1, if b = |C| then b^2 = c^2 and hence a^2 - b^2 = 0 i.e. a^2 = b^2. Hence, sufficient.

Stmt2 is the repeat of question itself....hence sufficient.
VP
Joined: 21 Jul 2006
Posts: 1455
Re: HOW TO SOLVE THIS? [#permalink]

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30 Aug 2008, 14:32
scthakur wrote:
I will go with C.

The question is really asking whether square of a is the same as that of b.

From stmt 1, if b = |C| then b^2 = c^2 and hence a^2 - b^2 = 0 i.e. a^2 = b^2. Hence, sufficient.

Stmt2 is the repeat of question itself....hence sufficient.

you said that each statement is suff. but you choose C as your answer?
VP
Joined: 21 Jul 2006
Posts: 1455
Re: HOW TO SOLVE THIS? [#permalink]

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31 Aug 2008, 05:11
so what's the OA to this question?
Manager
Joined: 09 Jul 2007
Posts: 236
Re: HOW TO SOLVE THIS? [#permalink]

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31 Aug 2008, 05:25
IMO E.

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

1) b = |c|

If we fit this in the above equation, then a^2 - b^2 =0 => a= + or - b

So A alone not sufficient ( as a =|b| menas a is +ve )

2) b = |a|

b is + ve . but a can be +ve or -ve. So reverse is not true.

Even after combining, a =+ or - b and b = +ve which does not indicate if a is + ve or not.
VP
Joined: 21 Jul 2006
Posts: 1455
Re: HOW TO SOLVE THIS? [#permalink]

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31 Aug 2008, 06:07
arjtryarjtry, what's the OA? almost all of us have come up with a different answer. I need to know the OA so that i can sleep well tonight. hehe...
Senior Manager
Joined: 06 Apr 2008
Posts: 393
Re: HOW TO SOLVE THIS? [#permalink]

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31 Aug 2008, 06:45
IMO E)

a = |b| statement shows that a is always +ve but a can be -ve or + ve from both statements
VP
Joined: 21 Jul 2006
Posts: 1455
Re: HOW TO SOLVE THIS? [#permalink]

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31 Aug 2008, 08:52
ok guys, I managed to find the OA to this question. The OA is E.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: HOW TO SOLVE THIS?   [#permalink] 31 Aug 2008, 08:52
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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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