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Bunuel
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Shouldn't it be D since a≠c implies that |a| ≠ |c| for any values of a and c ? Please correct me if I'm wrong.

c ≠ a does not necessarily mean that |a| ≠ |c|. For example, -1 ≠ 1 but |-1| = |1|.
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Is |a| = |c|?

(1) a + b = b–c
(2) –c ≠ –a

(1) -----

a+b = b-c
=> a = -c
=> |a| = |-c| , putting both side mod
=> |a| = |c| , since any value inside mod is non-negative. SUFFICIENT

(2) -----
–c ≠ –a
=> a≠c
=> |a| ≠ |c| . NOT SUFFICIENT
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Shouldn't it be D since a≠c implies that |a| ≠ |c| for any values of a and c ? Please correct me if I'm wrong.


Its true for +ve and -ve values of a number
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Is |a|=|c|?

1) a = –c --> |a|=|-c|=|c|
SUFFICIENT

2) –c ≠ –a
If c=2 and a=-2, then –c ≠ –a but |a|=|c|.
If c=2 and a=1, then –c ≠ –a and |a|≠|c|
NOT SUFFICIENT

FINAL ANSWER IS (A)

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