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30 Oct 2007, 13:30
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a^2 - b^2 = b^2 - c^2 . Is a = |b| ?
1. b = |c|
2. b = |a|
Please provide explanations for your answers
1. b = |c|
2. b = |a|
Please provide explanations for your answers
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30 Oct 2007, 13:44
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(D) for me 
a^2 - b^2 = b^2 - c^2
a = |b|?
<=> a = b or a = -b ?
stat 1
o b = |c|
<=> b^2 = c^2
Then,
o a^2 - b^2 = b^2 - c^2
<=> a^2 - b^2 = c^2 - c^2
<=> a^2 = b^2
<=> a = b or a = -b
SUFF.
stat 2
b = |a|
Implies
o b = a
or
o b = -a <=> b = -a
SUFF.
a^2 - b^2 = b^2 - c^2
a = |b|?
<=> a = b or a = -b ?
stat 1
o b = |c|
<=> b^2 = c^2
Then,
o a^2 - b^2 = b^2 - c^2
<=> a^2 - b^2 = c^2 - c^2
<=> a^2 = b^2
<=> a = b or a = -b
SUFF.
stat 2
b = |a|
Implies
o b = a
or
o b = -a <=> b = -a
SUFF.
01 Nov 2007, 14:16
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a = |b|?
Isnt the answer E?
(1) b = |c|
This gives us a^2 = b^2
Assume a = 2, b = -2 then 2 = |-2| is CORRECT.
Assume a = -2, b = 2 then a^2 = b^2 is satisfied.
But in this case a = |b| gives -2 = |2| which is INCORRECT.
Hence, not sufficient.
(2) b = |a|
This satisfies a = -2, b = 2 since 2 = |-2|
But as shown above a = |b| gives -2 = |2| which is INCORRECT.
Hence, not sufficient.
Putting (1) and (2) together we still get the same results with a = -2, b = 2.
Isnt the answer E?
(1) b = |c|
This gives us a^2 = b^2
Assume a = 2, b = -2 then 2 = |-2| is CORRECT.
Assume a = -2, b = 2 then a^2 = b^2 is satisfied.
But in this case a = |b| gives -2 = |2| which is INCORRECT.
Hence, not sufficient.
(2) b = |a|
This satisfies a = -2, b = 2 since 2 = |-2|
But as shown above a = |b| gives -2 = |2| which is INCORRECT.
Hence, not sufficient.
Putting (1) and (2) together we still get the same results with a = -2, b = 2.
Fig
