Is |x| = y-z?

IMO C

First Statement:

x + y = z
x = z - y

Ins.

Second Stmt.

x < 0

Ins.

Together

Sufficient because z - y is opposite of y - z

To further elaborate:

absolute value must be positive, but we do not know if y - z is pos or if z - y is pos. Since x is negative, we know that y - z is pos

Hence the statement is true

The easiest way to crack mod questions is by doing the following:

|x| = x (only if x > 0)
|x| = -x (only if x < 0)

Here, it's pretty clear that 2 all by itself doesn't do much. However, if you have that |x| = y - z and x < 0, then -x = y - z, so z = x + y, and you get 1.

Domnu wrote:The easiest way to crack mod questions is by doing the following:

|x| = x (only if x > 0)
|x| = -x (only if x < 0)

Here, it's pretty clear that 2 all by itself doesn't do much. However, if you have that |x| = y - z and x < 0, then -x = y - z, so z = x + y, and you get 1.

Domu, isn't it true that what ever be the sign of x [-ve or +ve] the mod of x will always be positive? I mean, lets say, x= -4 so |x|=> |-4|= 4. Could you please throw some more light on it? Got confuse after seeing this line

|x| = -x (only if x < 0)

Yes, what you say is true.. |x| > 0. But! Look at this:

|x| = -x

This doesn't mean that there are no solutions.. what if the right side is positive? That is, what if

-x > 0

which is the same thing as writing x < 0? Try putting in a few values:

|-2| = -(-2) = 2 (correct!)

|-pi| = -(-pi) = pi (correct!)

etc.

Generally, the definition of mod is the following:

|x| = x only if x is 0 or positive
|x| = -x only if x is 0 or negative