Is |x|=y-z? (1) x+y=z (2) x<0

I think the answer should be D. Here is why:

|x|=y-z


We have 2 different scenarios here, if x is positive then x= y-z, and if x is negative then x=z-y

since we rather have the y-z in the question, the question is really asking whether x is positive. so let's take a look at each statement:

(1) says that x=z-y, since we know what z-y means that x is negative, it answers the question as a "no", X is not positive, but rather a negative.

(2) directly says that x is negative, so it answers the question.

C is the correct ans. source of the question is OG11.

then can somebody explain what's wrong with my logic? How come sometimes when you come across questions with absolute values, you would split into positive and negative, but then you're not allowed in this question? for example:

|x-3|>1

so here, if x-3 is positive, then x>4, but if x-3 is negative, then x<2. So how come we're allowed to do so in this example, but then it's wrong to do the same in your posted question?

thanks


EDIT: Ah, I get it now. What the question is really asking is whether y-z is positive or even zero. It's not like the question mentioned this equation as a fact, but rather, this equation is under suspicion.

(1) x+y=z --->x=z-y, but we don't know whether this expression is positive, negative, or even zero

(2) x <0 ----> x is negative. It doesn't help us because we need to find a link between x and y-z. It doesn't matter what x is by itself because any sign within the absolute sign will always be positive or even zero. What we really need to know is whether the expression y-z is positive or zero.

(1&2) when -x=z-y, because x is negative in this equation, we know that z must be smaller than y, so when you reverse it to y-z, you know for sure that the expression will be positive!

Exactly, same reasoning I got, after reading OE.

I read the question as "Is the difference between y and z positive and does it equal absolute value of x?"

Stmt 1 simply says that difference between y and z is -x. It does not say whether this difference is positive or not. That is why, it is not sufficient. If the question provides additional information that x is positive or x is negative or zero, then stmt 1 can be sufficient.

Stmt 2 on its own is not sufficient. It just says that x is negative. It does not say anything about the difference between y and z being equal to x.

However, combining the two gives the answer.