if zy<xy<0, is |x-z| + |x| = |z|? strange, for some : DS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 01:47

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

if zy<xy<0, is |x-z| + |x| = |z|? strange, for some

Author Message
Current Student
Joined: 31 Aug 2007
Posts: 369
Followers: 1

Kudos [?]: 127 [0], given: 1

if zy<xy<0, is |x-z| + |x| = |z|? strange, for some [#permalink]

Show Tags

20 Nov 2007, 17:20
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

if zy<xy<0, is |x-z| + |x| = |z|?

strange, for some reason it is not coming out as i type it...

statement 1--z is less than x
statement 2--y is greater than 0

Last edited by young_gun on 20 Nov 2007, 18:01, edited 5 times in total.
Manager
Joined: 03 Sep 2006
Posts: 233
Followers: 1

Kudos [?]: 19 [0], given: 0

Show Tags

20 Nov 2007, 19:48
My ans is C:

1) Z < X
it means than Z and X can either be both +ve or both -ve
***** if +ve:
Z < X
3 < 5
|5 - 3| + |5| = |5| NO

***** if -ve:
Z < X
-5 < -3
|-3 - (-5)| + |-3| = |-5| YES

Hence 1) is insuff

2) Y > 0, this means that Z and Y are -ve
Z < X
-5 < -3
|-3 - (-5)| + |-3| = |-5| YES

Z > X
-1 > -100
|-100 - (-1)| + |-100| = |-1| NO

Hence 2) is insuff

Together: suff
Manager
Joined: 25 Jul 2007
Posts: 108
Followers: 1

Kudos [?]: 19 [0], given: 0

Show Tags

20 Nov 2007, 20:06
young_gun wrote:
if zy<xy<0, is |x-z| + |x| = |z|?

strange, for some reason it is not coming out as i type it...

statement 1--z is less than x
statement 2--y is greater than 0

First of all, we note that x,y or z cannot be equal to 0.

Statement 1: Sufficient.

If z < x, then both 'x' and 'z' have to be negative and 'y' has to be positive. ( since zy < xy < 0 )

In such a scenario, |x-z| + |x| will always be equal to |z|.

Statement 2: Sufficient.

If y is greater than 0, it again implies that both 'x' and 'z' are negative. ( since zy < xy < 0 ).

Therefore answer is D. Both are sufficient.
Current Student
Joined: 31 Aug 2007
Posts: 369
Followers: 1

Kudos [?]: 127 [0], given: 1

Show Tags

21 Nov 2007, 06:28
jbs wrote:
young_gun wrote:
if zy<xy<0, is |x-z| + |x| = |z|?

strange, for some reason it is not coming out as i type it...

statement 1--z is less than x
statement 2--y is greater than 0

First of all, we note that x,y or z cannot be equal to 0.

Statement 1: Sufficient.

If z < x, then both 'x' and 'z' have to be negative and 'y' has to be positive. ( since zy < xy < 0 )

In such a scenario, |x-z| + |x| will always be equal to |z|.

Statement 2: Sufficient.

If y is greater than 0, it again implies that both 'x' and 'z' are negative. ( since zy < xy < 0 ).

Therefore answer is D. Both are sufficient.

can you/someone pls elaborate the bold section?
Manager
Joined: 25 Jul 2007
Posts: 108
Followers: 1

Kudos [?]: 19 [0], given: 0

Show Tags

21 Nov 2007, 07:21
young_gun wrote:
jbs wrote:
young_gun wrote:
if zy<xy<0, is |x-z| + |x| = |z|?

strange, for some reason it is not coming out as i type it...

statement 1--z is less than x
statement 2--y is greater than 0

First of all, we note that x,y or z cannot be equal to 0.

Statement 1: Sufficient.

If z < x, then both 'x' and 'z' have to be negative and 'y' has to be positive. ( since zy < xy < 0 )

In such a scenario, |x-z| + |x| will always be equal to |z|.

Statement 2: Sufficient.

If y is greater than 0, it again implies that both 'x' and 'z' are negative. ( since zy < xy < 0 ).

Therefore answer is D. Both are sufficient.

can you/someone pls elaborate the bold section?

Practically, just put in couple of negative values for 'x' and 'z' and you will find out for yourself.

Alternatively, here's the conceptual explanation.

We know that 'x' and 'z' are negative.

Therefore |x-z| is basically the same as |z| - |x|. (e.g: |-2 - (-3)| = |-3| - |-2|
i.e. |x-z| = |z| - |x| + |x| = |z|

Hope this helps.
SVP
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 149 [0], given: 0

Show Tags

21 Nov 2007, 09:21
(D) for me too

|x-z| + |x| = |z|?

zy<xy<0

Implies that:
o zy - xy < 0
<=> y*(z-x) < 0
<=> y*(x-z) > 0

That means : sign(y) = sign(x-z)

Stat 1
We have :
o z < x
<=> x-z > 0

That means : y > 0.

As y > 0, with zy<xy<0, we now know that z < 0 and x < 0.

Finally,
o |x-z| + |x|
= (x-z) + (-x) as x-z > 0 and -x > 0
= -z
= |z| as z < 0

SUFF.

Stat 2
We have y > 0

That means x-z > 0.

Again, as y > 0, with zy<xy<0, we now know that z < 0 and x < 0.

Finally,
o |x-z| + |x|
= (x-z) + (-x) as x-z > 0 and -x > 0
= -z
= |z| as z < 0

SUFF.
21 Nov 2007, 09:21
Display posts from previous: Sort by