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

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TheChakra

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

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

TheChakra

Anonymous wrote: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

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
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Posts: 125
Joined: Fri Jun 05, 2009 7:46 am

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

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.