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

[TheChakra]

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

OA = E

I am unable to rephrase this question. There are 2 possibilities, z is between x and y (the ask) and z is left of x. Is that correct rephrasing? I was just lost on the clues. Even though the answer is E, the clues normally take you closer to solving the problem. I don't know what the two clues are doing here?

1. xyz < 0 -- so either all three or one of the three is negative
2. xy < 0 -- either x or y is negative, BUT not both.

1 and 2 combined - either x or y are negative.. How does that bring me close the solution? What MORE information could have helped me answer the question here?

[Guest]

try to draw out the cases. for example

(1) xyz < 0 and |xy| > |xz| . this implies the following are possible (with the Y-axis indicated as the vertical bar)

yx | z
z | xy
xz | y
yz | x

(2) xy < 0 means that x & y are on opposite sides of the vertical axis. and |xy| > |xz|

y | zx
y | xz
x | zy


the cases illustrate the answer

[TheChakra]

try to draw out the cases. for example

(1) xyz < 0 and |xy| > |xz| . this implies the following are possible (with the Y-axis indicated as the vertical bar)

yx | z
z | xy
xz | y
yz | x

(2) xy < 0 means that x & y are on opposite sides of the vertical axis. and |xy| > |xz|

y | zx
y | xz
x | zy


the cases illustrate the answer

Thanks! you actually missed a few scenarios which would give you E ((y| xz) in both the cases implying z need not be between x and y.)

[sudaif]

we are given abs(x-y)>abs(x-z)
question is : does z lie b/w x and y?

statement 1)
xyz<0 ----->possible scenarios
++- in this case z will not lie b/w x and y
+-+ in this case z could lie b/w x and y or could lie to the right of z
-++
given the two possibilities, this statement is insuff

statement 2)
xy<0
+-
-+
but this statement tells us nothing about z
so insuff

statement 1 + statement 2)
xy<0 xyz<0
+- +-+ in this case, z could be on either side, note y<0
-+ -++ in this case, z must lie b/w x and y

AGain we have two possibilities. Thus insuff.

Answer should be E

Instructors, can you please corroborate?

[RonPurewal]

there's a nice solution here:

post2446.html#p2446