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by GMATGuruNY » Fri Aug 15, 2014 5:50 am
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?
a) xyz < 0
b) xy < 0
When no order is specified, consider different -- especially NON-ALPHABETIC -- orderings of the given points.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..................z=9.....x=10
Here, z lies between x and y.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..............................x=10....z=11
Here, z does NOT lie between x and y.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Nijo » Fri Aug 15, 2014 8:30 pm
Hi Mitch
Thank you, but what do you mean by non alphabetic numbering?
Also when I started off with this question, I stated thinking of multiple possibilities like negative z, positive x, positive y etc.
In the middle of all the possible permutations, combinations I got lost and ended up wildly guessing.
Any thoughts on whats the best way to approach these questions - by assigning signages? Looking at values? Start with all positive values?
Thanks very much!
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by GMATinsight » Sat Aug 16, 2014 10:12 am
Nijo wrote: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

OA is C
Question : Does z lie between x and y on the number line??

Statement 1) xyz < 0

Inference 1: Exactly one of x,y and z is Negative
If y is Negative, x and z are positive and x>z which will also validate that distance xy > Distance xz
then z lies between y and x

Inference 2: All of x, y and z are Negative
such that y<x<z such that Distance y=-10, x=-2, z=-1 then z DOESN'T lie between y and x
INSUFFICIENT

Statement 2) xy < 0
No information about z therefore
INSUFFICIENT

Combining the two statement
Exactly one of x,y and z is Negative
If y is Negative, x and z are positive and x>z which will also validate that distance xy > Distance xz then z lies between y and x

and If y is Negative, x and z are positive and x<z [y=-10, x=2, z=3] then z DOESN'T lie between y and x
INSUFFICIENT

Answer: Option E
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by [email protected] » Sun Aug 17, 2014 12:45 am
Hi Nijo,

When Mitch mentioned "non-alphabetic ordering", he meant that when you have multiple variables (e.g. X, Y and Z), they're not necessarily in order from least to greatest (maybe X is the smallest of the 3, but maybe it's NOT. It could be the biggest of the 3 or it could be the second biggest). Unless a prompt gives you the specific restriction that one variable is smaller than another, you don't have to follow the "order" of the variables.

In this question, there are almost no restrictions, which should get you thinking that the situation is probably INSUFFICIENT. You don't even have to come up with that many examples to prove it.

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