Distance between x and y is greater than distance between x

Question

Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0

Please provide explanation for your answer. Thank you!

fluke · Answer

1. xyz < 0 Either only one of {x, y, z} is -ve or all three are negative. Let me consider former(one -ve): y=-1, z=0.9, x=1; |x-y|>|x-z|, z in between OR y=-1, z=1.1, x=1; ; |x-y|>|x-z|, z not in between Not Sufficient. 2. xy < 0 Only one of x and y is -ve. No information about z. Not Sufficient. Both the cases discussed in St1 above hold good. Combining both; Both the cases discussed above hold good. Ans: "E"

gmat1220 · Answer

I think if you realize the spatial arrangement of x y z on the numberline then this is easy

1. 2 cases possible

x | z y where | is the zero. z is between x and y. The answer is YES

or

z x | y

z is NOT between x and y. The answer is NO

Insufficient

2. This is useless. Since there is no constraint on z. z may bet or may not between x and y. No need to evaluate. Hence insufficient

Combining 1) + 2) Insufficient

2 cases possible

x z | y

The answer is YES

or

y | x z

The answer is NO

Hence E.

PS : In almost all the questions with spatial arrangement of three points x y z, I have very few answers with C. Most of these DS questions are inconclusive. If you are short of time and have just 30 secs - ensure that C is not going to work and you are good.

amit2k9 · Answer

a x,y,z all can be negative | x or y or z can be negative. Not sufficient.

b x|y negative giving nothing about Z.

a+b

x= -10 y = 10 , z = 1 Z is in between. yes
y= -10 x = 1, z=2 Z is outside. No.

Hence E.

subhashghosh · Answer

(1)

z--------0---x----------------y

x--------0---z----------------y

Insufficient

(2)

x--------0---z----------------y

z-----x--------0-------------------y

Insufficient

(1) + (2)

From Diagram in (2)

Insufficient

Answer - E

adhithya · Answer

question states that d(x,y)>d(x,z) also from (1) and (2) we know that z is positive 
(as xy<0=>z>0)
thus looking at above conditions we can say that z is between x and y
where am i going wrong

Bunuel · Answer

OPEN DISCUSSION OF THIS QUESTION IS HERE: on-the-number-line-the-distance-between-x-and-y-is-greater-127014.html

Distance between x and y is greater than distance between x

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