Number line

[selango]

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

A)xyz<0

B)xy<0


OA E

[liferocks]

From 1
two of x,y and z has same sign.
So
scenario 1: if x and y has same sign and z different (ex x and y +ve and z -ve) then z does not lie between x and y
scenario 2: if x and z has same sign and y different and z>x (ex x and z +ve and y -ve) then z does not lie between x and y
scenario 3:if x is negative and z and y +ve ,z lies between x and y ..not sufficient

from 2
x and y has different sign..no information about z..not sufficient

combining,
scenario 2 and 3 of condition 1 shows this and its not sufficient

Ans option E

[tpr-becky]

We need some method of determining where exactly these numbers lie in relation to each other.

statement 1 says that either one of the numbers is negative or all three are negative - but it give no indication to which one - x could be between y and z or z could be between y and x. Insufficient

statemetn 2 - says that either x or y is negative - this doesn't say anything about z so we dont' know.

if you put them together you know that x or y is negative and z is positive but we don't know if x is in the middle or if z is in the middle - becuase there is no way to determine the relationship between the numbers the answer is E.

[selango]

We need some method of determining where exactly these numbers lie in relation to each other.

statement 1 says that either one of the numbers is negative or all three are negative - but it give no indication to which one - x could be between y and z or z could be between y and x. Insufficient

statemetn 2 - says that either x or y is negative - this doesn't say anything about z so we dont' know.

if you put them together you know that all three numbers are negative but we don't know if x is in the middle or if z is in the middle - becuase there is no way to determine the relationship between the numbers the answer is E.

Becky,

one doubt here..if we combine 2 stmts,if xy is -ve,z can be +ve so that xyz<0..


Pls clarify

[tpr-becky]

correct, I have edited my post - but the reasoning still stands.

[Patrick_GMATFix]

We know that XY is longer than XZ. Is Z between X and Y?

(1) We either have all three negatives, or 1 negative and 2 positives. We could have x=-1, y=-3 and z=-2. In this case, the answer to the original Q would be YES. on the other hand we could have x=-1, y=-3 and z=-0.5. In this case, the answer to the original Q would be NO Z is not between the others. Insufficient

(2) This tells us nothing about the location of Z. but tells us that either X or Y, but not both, is negative. Insufficient.

Merging the statements, we can deduce that either:
x is negative; y is positive; z is positive. OR
y is negative; x is positive; z is positive.

It's still possible to come up with values that answer the original Q with a YES (Z is between the other 2) or a NO (Z is to the right of the other 2, but really close to X which is in the middle). We don't have sufficiency. The answer is E.

This is GMATPrep question 1037. You can practice similar questions if you have access to the Solutions Engine drill generator by selecting topic="Inequalities & Absolute Values" and difficulty="600-700"


Good luck,
-Patrick