Num Prop SG,ApndxA, pg127 If xyz not=0, is 3x/2+y+2z=7x/2+y?

[AndrewF994]

This is a pretty simple question from the Number Properties Strategy Guide (6 ed), Appendix A: Data Sufficiency, page 127.

On the DS process overview, it discusses rephrasing the question:

If xyz does not = 0, is 3x/2 + y + 2z = 7x/2 + y?

(1) y = 3 and x = 2
(2) z = -x

Per the guide, the stem simplifies to:

z = x?

The correct answer is (B), which confuses me a bit. The logic in the guide is that "None of the variables is 0, so if z = -x, the those two numbers cannot be equal to each other. This statement is sufficient, to answer the question: no, z does not equal x."

I get that z does not equal x. But, my thought process was that although statement (1) is not sufficient alone, if x = 2, and z = -x, then z does not equal x, which is why I selected (C) - both statements are sufficient together.

So, I know that theoretically I don't need to actually solve for the value, but do I need to take it more literally, that z does not equal x because z is positive and x is negative? As in, would it say - z = -x if z and x were equal?

In my mind, z could be any number, other than 0, and x could be any number, but negative...Maybe I am just confusing myself and sound like a newb. I chose (C) because if x = 2, then z = -2, and therefore not equal to x.

Thanks in advance.

[Chelsey Cooley]

I get that z does not equal x. But, my thought process was that although statement (1) is not sufficient alone, if x = 2, and z = -x, then z does not equal x, which is why I selected (C) - both statements are sufficient together.

This is where your error happened. On DS, always consider each statement individually before you ever consider choosing (C). That's because (C) doesn't just say "both statements are sufficient together" - it actually says "both statements are sufficient together, and neither statement is sufficient on its own." So if (2) proves that Z does not equal X, then the right answer has to be B (well, or it could be D, except that you've already decided that (1) is insufficient).

[AndrewF994]

Chelsey,

Thanks for your response! Glad to see you're back.

I think I may have just confused myself, or probably just suffer from horrible algebra. I guess what I had thought was that if z = -x, then how do I know that that can't be the same number? As in, z could be anything, and x could be anything, it just means that whatever x is, z = the negative form...

So if I don't know what x is, then can I say with certainty what Z is? But if I know what x is, and its the number 2, and z = -x, thus -2, then z does not equal x.

But I guess from a 1:1 comparison, if the question is does z = x? and (2) says z = -x, then I guess I don't need to worry about going any further, because right there I can say no, they are different...

I think I just got lost in solving.

Thanks,
Andrew

[RonPurewal]

But I guess from a 1:1 comparison, if the question is does z = x? and (2) says z = -x, then I guess I don't need to worry about going any further, because right there I can say no, they are different...

the blue thing only works because x = z = 0 has already been ruled out (by the conditions specified at the beginning of the problem).
if zero were allowed, then the blue logic would no longer work.

you may be aware of this already, but i'm just including it for the sake of completeness.