On the number line, the distance between x and y is greater

[borcho]

On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?

1) xyz <0

2) xy<0

This is a DS question. Please provide the shortest solution.

[Luci]

I think the answer is E) but it is hard to explain without drawing the line....

[Guest]

The answer is E I belive.

Scenario A ) where XYZ < 0.

2 positives 1 negative
3 negatives.

For three negatives on the number the order can be z, x, y, 0...or x, z, y, 0.

So A is insufficient.

Scenario B) hwere XY < 0.

One negative one positive. So the order can go. x 0 z y...or z x 0 y. So B is insufficient.

Scenario A+B.

If X and Y are both of oppositie signs (XY<0)..then Z has to be postive in order for XYZ < 0.

So One Negative and two positives.

Order can be.....x 0 z y...or y 0 x z.

Thus E.

[StaceyKoprince]

Yep, you've got it! This is harder to follow without drawing a number line, so those reading the above explanation may want to draw a number line and follow it through.

[sachin.w]

I have been trying not to pick up the pen to solve such Questions.
visualized the entire thing . got E as the answer. though it took some time..

Hope mental process will get better with time and practice.

Just hope I am doing the right thing.

[RonPurewal]

I have been trying not to pick up the pen to solve such Questions.
visualized the entire thing . got E as the answer. though it took some time..

Hope mental process will get better with time and practice.

Just hope I am doing the right thing.

this is not "the right thing". by doing everything in your head and not writing stuff down, you're not really accomplishing anything other than making everything harder (and slower!).

fact: the error rate of mental math is over 2,000% greater than the error rate of math on paper.

question:
what do you think you are gaining by doing everything in your head?
the usual response is "i think it's faster that way". this is false -- doing the work on paper is faster than trying to do it in your head -- but, here, you've even said that the mental process takes longer.
i'm glad you recognize that; because you do, though, i'm not seeing any reason why you wouldn't just pick up the pen and draw a diagram and/or write stuff down.
why not?

[sachin.w]

I found that by not using my pen and paper, I tend to have the grip of all the conditions of DS that I am supposed to check whereas by using a pen and paper, I keep searching for the different conditions that I have jotted down.

and I believed my mind can become sharper by doing so :) well it might but as you said , error rate is high . so I might well stop doing this and rethink of jotting down things clearly on the paper so that I don't have to search the different conditions.

Thanks a lot for letting me know this.

[tim]

thanks for the advice, Ron!

[WillS10]

So, for this question, the first sentence in the question stem is not necessary?
---On the number line, the distance between x and y is greater than the distance between x and z. ---

Will

[RahulS203]

My online tests are not active for few months, I mailed you few month back but haven't received any communication.
Please activate soon its showing my subscription is going to expire soon.

I think there is some problem as my subscription is active still I'm not able to use the tests
Feel like cheated

Please Help

[tim]

So, for this question, the first sentence in the question stem is not necessary?
---On the number line, the distance between x and y is greater than the distance between x and z. ---

Will

Well, technically, anytime the answer is E, any information given in the question stem is not *necessary* in order to arrive at the answer choice. This does not mean you should neglect to consider it in your analysis of the problem though, because you have no a priori reason to know that the answer will end up being E.

[tim]

My online tests are not active for few months, I mailed you few month back but haven't received any communication.
Please activate soon its showing my subscription is going to expire soon.

I think there is some problem as my subscription is active still I'm not able to use the tests
Feel like cheated

Please Help

I'm not sure what could possibly have led you to believe that this was the appropriate place to ask this question. Please call the New York office, and they will be able to answer these questions for you.

[RonPurewal]

^^ +1 (212) 721-7400
or you can e-mail gmat@manhattanprep.com

[BrettB487]

Question here: Does the statement "the distance between x and y is greater than the distance between x and z mean that x - y > x - z? And consequently that - y > - z / y < z?

Thanks

[RonPurewal]

"the distance between x and y" could be either x – y or y – x, depending on which is greater.
likewise, "the distance between x and z" could be either x – z or z – x.

remember, GMAC's question writers don't engage in deliberate obfuscation. if a problem is stated in "awkward-looking" words rather than in terms of algebra, there are probably multiple algebraic interpretations.