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

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On the number line, the distance between x and y is greater [#permalink] New post 05 Oct 2007, 23:48
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A
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C
D
E

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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
Senior Manager
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 [#permalink] New post 06 Oct 2007, 01:11
Both the conditions together are sufficient to asnwer the Q

info 1: INSUFF
info 2: x & y are of opposite signs though z could b positive or negative so INSUFF

info 1 + info 2: SUFF - x & y are of opposite signs & z is positve so - z must lie between x & y for the consdition xy > xz to hold!

Last edited by singh_amit19 on 06 Oct 2007, 01:46, edited 1 time in total.
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 [#permalink] New post 06 Oct 2007, 01:19
Assume z=2 , y=-1 and x=3

-1*-3 < 0 ---> true

2*-1*3 < 0 ---> true

from stem:

|x-y| > |x-z|

|3+1| > |3-2| ---> true

In order for stem to be true

x > y
y < z

or

x < y
y > z

either way z is in the middle !

the answer is (C)

:)
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 [#permalink] New post 06 Oct 2007, 08:52
OA is E.. can someone please explain?
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Re: DS: distance [#permalink] New post 06 Oct 2007, 21:17
1. either all x, y and z are -ve or two of them +ve and one -ve. Insuff.

2. x and y are of opposit sign. In suff.

Combine. z is +ve. x and y are different sign.


say y is -ve(-100) and x is +ve (+10)

then stem stem |x-y| > | x-z|
could be satisfied when z= 20 or z=0.
Insuff.

E.
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Re: DS: distance [#permalink] New post 07 Oct 2007, 01:02
mexicanhoney wrote:
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


easiest approach is to draw it:

from stem we have those options
..-z...-x........0.........y..
...-x....0..z............y...
-..-y.......0.....x...z...
there are lots of those imaginations if u cont. but enough for now

1. so one of x,y and z is negative. the above laready shows several options which doesnt show any suff. of xyz<0

2. xy<0 now draw again.
.....-x...-z...0.....y
..-z...-x.....0.....y
so insuff.

together:

....-x...0...z......y...
....-y...0........x..z..
so not suff
E
Re: DS: distance   [#permalink] 07 Oct 2007, 01:02
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