I double checked the question. It is correctly copied.
I myself could not get the twisted logic behind the official explanation and hence posted the question here.
This is what the official explanation is:
Explanation: There are two ways for the equation in the question to be
true. If a is positive, then it is true if a = b - c. If a is negative, then it is true
if -a = b - c, or put another way, a = c - b. To answer the question, we need
to know whether a is positive or negative, and if the corresponding equation is
true.
Statement (1) is insufficient. a+c \(\neq{b}\) is the same as a \(\neq{b}\) - c, which means
that, if a is positive, the answer is "no." However, it doesn’t tell us what the
answer is if a is negative.
Statement (2) is also insufficient: it gives us the sign of a, but nothing about
how it relates to b and c.
Taken together, the statements are sufficient. Since we know a is negative,
we know the question asks, "Is a = c - b ?" (1) tells us that that is not true,
so the answer is "no." Choice (C) is correct.
chetan2u wrote:
longranger25 wrote:
Is |a| = b - c ?
(1) a + c\(\neq{b}\)
(2) a < 0
Source:
Jeff SackmanPl recheck the question
In present state it is E..
Either
Statement I is a+b\(\neq{c}\)
Or
Statement II would be a>0
Is |a|=b-c?
If a>0, a=b-c
If a<0, a=c-b
1) \(a+c\neq{b}............a\neq{b-c}\)
But a can be equal to c-b
Insufficient
2) a<0..
So from above
a could be equal to c-b
Insufficient
Combined.
If a=c-b... Yes otherwise No
Insufficient
E
But had statement II been a>0
Combined..
a>0, so only possibility of yes is if a=b-c
But statement I gives \(a\neq{b-c}\)
So Ans is always NO
Sufficient
Then C