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