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Re: GMATprep Inequalities [#permalink]
28 Jan 2010, 02:51

6

This post received KUDOS

An easy way to approach this ineq will be to analyze that: |x-z| + |x| = |z| means |z-x| = |z| - |x|. |z-x| is the distance between z and x on number line. It can only be equal to |z| - |x| if both z and x have the same signs.

a) z < x - implies that y > 0 because zy < xy. If y > 0 then z < x < 0. Therefore both have same signs. SUFF

b) y>0 then z < x < 0. Therefore both have same signs. SUFF

Re: GMATprep Inequalities [#permalink]
28 Jan 2010, 05:14

3

This post received KUDOS

Expert's post

This question was discussed before here is my post from there:

This is not a good question, as neither of statement is needed to answer the question, stem is enough to do so.

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

Look at the inequality zy<xy<0:

We can have two cases:

A. If y<0 --> when reducing we should flip signs and we'll get: z>x>0. In this case: as z>x --> |x-z|=-x+z; as x>0 and z>0 --> |x|=x and |z|=z.

Hence in this case |x-z|+|x|=|z| will expand as follows: -x+z+x=z --> 0=0, which is true.

And:

B. If y>0 --> when reducing we'll get: z<x<0. In this case: as z<x --> |x-z|=x-z; as x<0 and z<0 --> |x|=-x and |z|=-z.

Hence in this case |x-z|+|x|=|z| will expand as follows: x-z-x=-z --> 0=0, which is true.

So knowing that zy<xy<0 is true, we can conclude that |x-z|+|x| = |z| will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that z<x, hence we have case B.

Statement (2) says that y>0, again we have case B.

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink]
17 Dec 2013, 03:17

I solved this question on number line, we can first analyze this eq |x-z| + |x| = |z|? This equality is only possible, if x and z are on the same side of the number line.

(-) ----z----x----0--- or ---0-----x----z---- (+)

|distance between xandz| + |distance of x from origin| = |distance of z from origin|

given zy<xy<0 which can happen in two case.

z x y - - + zy negative xy negative < both less than 0 + + - zy negative xy negative < both less than 0

Therefore we don't even need option 1 and 2 to validate this |x-z| + |x| = |z|.

Answer : D

_________________

Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: WOULD: when to use? Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink]
10 May 2014, 11:04

using Statement 1 : from the question , zy < xy y(z-x)<0 ------- (A) Now statement 1 tells me that (z-x)< 0 . This implies Y>0 So, if zy < xy < 0 and Y>0 This implies Z & X < 0 mod (x-z) + mod (x) = X-Z (since Z-X<0) + (-X) = -Z = |Z|

Using Statement 2 : From (A), y(z-x)<0 Since from Statement 2 we know that y > 0 That implies (z-x)< 0 .

Hence D.

gmatclubot

Re: If zy < xy < 0, is |x-z| + |x| = |z|?
[#permalink]
10 May 2014, 11:04