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If zy < xy < 0, is |x-z| + |x| = |z|? (1) z<x>0

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If zy < xy < 0, is |x-z| + |x| = |z|? (1) z<x>0 [#permalink] New post 13 May 2007, 11:40
If zy < xy < 0, is |x-z| + |x| = |z|?

(1) z<x>0








OA is D
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 [#permalink] New post 13 May 2007, 11:41
oops...should be

(1) z is less than x
(2) y is greater than 0

Last edited by kookoo4tofu on 13 May 2007, 11:42, edited 1 time in total.
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 [#permalink] New post 13 May 2007, 11:42
can you post the rest of the question?
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 [#permalink] New post 13 May 2007, 12:35
|x-z| + |x| = |z|

can be rewritten as

|x-z| = |z|-|x|

Statement 1

whenever statement 1 is true |z|-|x| is negative.

|x-z| can never be negative

so we can say for sure that when z is less then x , the inequality is false.

sufficient

Statement 2

when y is grater then 0 then x,z have to be negative.

if x,z are negative and y is positive

when zy < xy < 0

then z<x

same info & logic as statement 1

sufficient

so the answer is (D).

:-D

Last edited by KillerSquirrel on 13 May 2007, 12:39, edited 1 time in total.
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 [#permalink] New post 13 May 2007, 12:39
My answer and other ones are here : http://www.gmatclub.com/phpbb/viewtopic.php?t=44909
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 [#permalink] New post 13 May 2007, 13:11
i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | =
| z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.
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 [#permalink] New post 13 May 2007, 13:36
ethan_casta wrote:
i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | =
| z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.


Actually, it's always true :)... For statment (1) & (2)... Have a look at my link :)
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 [#permalink] New post 13 May 2007, 13:41
ethan_casta wrote:
i. is not sufficient. you above KillerSquirrel have illustrated a case in which the questioned equation results in false. I'll illustrate one in which the questioned equation results in true: z = -3, x = -2, y = 1. | x - z | =
| z | - | x |.......So in this case, | -2 - (- 3) | = | -3 | - | - 2|, 1=1. So, of course, if we have one answer in which we get true and one in which we get false, statement i is insufficient. I get E as the answer then. Because you spotted that statement ii is equivalent to i. I didn't catch that part. I thought at first B was the answer.


yes ! you are right my logic is "non sequitur" :oops:
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Re: GMATPrep: abs [#permalink] New post 13 May 2007, 13:51
kookoo4tofu wrote:
If zy < xy < 0, is |x-z| + |x| = |z|?

(1) z is less than x
(2) y is greater than 0
OA is D


from i, if z is less than x, then x and z are -ve and y is +ve.. suff
from ii, if y is +ve, then again x and z are -ve and it is also sufficient.

So D.
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Abs value [#permalink] New post 13 May 2007, 14:07
Himalayan, the question is not that simple unfortunately.
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 [#permalink] New post 13 May 2007, 14:18
zy<xy<0...This means that z<x<0>0 and z>x>0 if y<0. In other words, both z and x have to be the same sign.

[1] z<x>0 Both z and x are negative - sufficient.

[2] kookoo4tofu wrote "y is greater than 0", but I believe the correct stmt is y<0. Using this stmt, both z and x are positive and therefore sufficient.

Answer: D
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Abs value [#permalink] New post 13 May 2007, 14:24
didn't you guys see that two cases have been advanced in which statement i produces a result of true and also a result of false? that disproves your claim.
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 [#permalink] New post 13 May 2007, 18:33
i checked the question again and statement 2 does say "y greater than zero"
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Re: Abs value [#permalink] New post 14 May 2007, 17:48
ethan_casta wrote:
Himalayan, the question is not that simple unfortunately.


you are right. i just laid down what i had in a quick calculation in my mind.
Re: Abs value   [#permalink] 14 May 2007, 17:48
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