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# If zy<xy<0, is |x-z|+|x|=|z|

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Manager
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If zy<xy<0, is |x-z|+|x|=|z| [#permalink]  26 Mar 2009, 09:53
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I think this was posted before but I can't find it. Can you please explain your answers:

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

1) z<x
2) y>0
Senior Manager
Joined: 16 Jan 2009
Posts: 361
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
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Re: DS GMAT Prep - Inequalities [#permalink]  26 Mar 2009, 11:48
If zy<xy<0, is |x-z|+|x|=|z|
1) z<x
2) y>0

we will be able to solve |x-z|+|x|=|z| if we get to know the signs of x and Z.
1) z<x , this just rephrases the given information which is not useful. No infrmation is specified regarding y , so we can not deduce the sign of x or z. INSUFFICIENT.

2)y>0
given : zy<xy<0
if y > 0 , x and z must be less than 0
also z<x<0.

now we can answer the inequality . SUFFICIENT.

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Lahoosaher

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Re: DS GMAT Prep - Inequalities [#permalink]  26 Mar 2009, 12:44
I agree - Statement 2 is sufficient - so the answer is B.

What is the OA?
Manager
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Re: DS GMAT Prep - Inequalities [#permalink]  26 Mar 2009, 13:13
Sorry guys, OA is D.
Manager
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Re: DS GMAT Prep - Inequalities [#permalink]  26 Mar 2009, 13:28
Accountant wrote:
I think this was posted before but I can't find it. Can you please explain your answers:

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

1) z<x
2) y>0

from given condition zy<xy

from (1), z<x --> y is positive --> z and x, both are negative and z < x. So, simplifying the equation:

LHS = |x-z|+|x| = x-z + (-x) = x-z-x = -z
RHS = |z| = -z (since z<0)

which implies, LHS = RHS , hence (1) is sufficient

from (2) , y> 0 --> z <0, x<0. Noe proceed the same way as above, that will give us a solution.

Both (1) and (2) are sufficient separately. Therefore, answer is (D).
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Re: DS GMAT Prep - Inequalities [#permalink]  26 Mar 2009, 18:01
krishan wrote:
Accountant wrote:
I think this was posted before but I can't find it. Can you please explain your answers:

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

1) z<x
2) y>0

from given condition zy<xy

from (1), z<x --> y is positive --> z and x, both are negative and z < x. So, simplifying the equation:

LHS = |x-z|+|x| = x-z + (-x) = x-z-x = -z
RHS = |z| = -z (since z<0)

which implies, LHS = RHS , hence (1) is sufficient

from (2) , y> 0 --> z <0, x<0. Noe proceed the same way as above, that will give us a solution.

Both (1) and (2) are sufficient separately. Therefore, answer is (D).

Agree 100%

You can rewrite the expression in the question as zy-xy<0 --> y(z-x) < 0. This leads to two options; either y<0 and z-x>0 or y>0 and z-x<0

From stat 1, you know z<x , so just quickly picking numbers, you see that the equality in question never holds.

From stat 2, you know z<x, and same approach as above gives the same result
Senior Manager
Joined: 16 Jan 2009
Posts: 361
Concentration: Technology, Marketing
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Re: DS GMAT Prep - Inequalities [#permalink]  27 Mar 2009, 02:18
I get it now.
Thanks pmenon.

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Lahoosaher

Re: DS GMAT Prep - Inequalities   [#permalink] 27 Mar 2009, 02:18
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