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# Is |x – y| > |x – z|?

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Intern
Joined: 17 Dec 2009
Posts: 5
Is |x – y| > |x – z|?  [#permalink]

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06 Jan 2010, 01:49
2
5
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:56) correct 39% (01:43) wrong based on 332 sessions

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Is |x – y| > |x – z|?

(1) |y| > |z|
(2) x < 0
Math Expert
Joined: 02 Sep 2009
Posts: 55609
Re: Modulus based DS question  [#permalink]

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06 Jan 2010, 03:24
1
4
raghuraoram wrote:
Hi could someone explain the steps to solve the below question?...

Is |x – y|>|x-z|?
1)|y|>|z|
2) z<0

OA= E[/color]

Basically the question is: "is the distance between x and y greater than the distance between x and z?"

(1) |y|>|z|, means y is farther from 0 than z, which gives us the following possible cases:

--y--------0---z-- or --y----z--0-- or --0----z------y or --z---0----------y--

Now depending on the position of x, the distance between x and y may or may not be greater than distance between x and z.

(2) x<0. Clearly insufficient as we know nothing about y and z:

---x----0---

(1)+(2) x<0 and |y|>|z|

--y------------x--0--z-- in this case |x - y|>|x - z|

BUT

--x--y---------z--0----- in this case |x - y|<|x - z|

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##### General Discussion
Intern
Joined: 17 Dec 2009
Posts: 5
Re: Modulus based DS question  [#permalink]

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06 Jan 2010, 05:08
1
Great explanation bunuel...you rock!!! is there any algebric way of solving this question...say, something usually done with the modulus based questions...|x – y|>|x-z|? this can be re-written as case 1 > x-y-x+z>0, therefore question reduces to whether z-y>0?....can you please throw some light on this alternate way. I perfectly understand and appreciate the detailed steps you already wrote down for me.
Manager
Joined: 05 Jul 2008
Posts: 128
GMAT 2: 740 Q51 V38
Re: Modulus based DS question  [#permalink]

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09 Jan 2010, 07:06
raghuraoram wrote:
Hi could someone explain the steps to solve the below question?...

Is |x – y|>|x-z|?
1)|y|>|z|
2) x<0

OA= E[/color]

|x – y|>|x-z|
(x-y)^2>(x-z)^2
(x-y)^2-(x-z)^2>0
(x-y-x+z). (2x-y-z) >0

So we must have the relationship between x,y,z to conclude |x – y|>|x-z|
E
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Joined: 29 Sep 2009
Posts: 374
GMAT 1: 690 Q47 V38
DS: Is |x - y|>|x - z|?  [#permalink]

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31 Oct 2010, 20:50
Is |x - y|>|x - z|?
(1) |y|>|z|
(2) x < 0

Is there a quick way of solving this problem?
By the time you get to C the clocks already rolled past the 2 min mark:
X Y Z |X-Y| |X-Z|
-5 -3 0 2 > 3
-5 -7 -3 2 < 4

E
Math Expert
Joined: 02 Sep 2009
Posts: 55609
Is |x – y| > |x – z|?  [#permalink]

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31 Oct 2010, 20:56
Senior Manager
Joined: 29 Sep 2009
Posts: 374
GMAT 1: 690 Q47 V38
Re: DS: Is |x - y|>|x - z|?  [#permalink]

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31 Oct 2010, 21:07
Bunuel wrote:

Check similar question for practice:

inequality-and-absolute-value-questions-from-my-collection-86939.html
math-ds-87926.html
ds7-93970.html
modulus-inequality-101660.html
absolute-values-101210.html

Hope it helps.

Clear!
I really hate re-posting questions, but for some reason when I search the question stem - the actual question doesn't show up in the list of searched results.
Manager
Joined: 08 Dec 2010
Posts: 165
WE 1: 4 yr IT

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13 Jan 2011, 00:43
Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0
in order to conclude that |x-y|>|x-z| or not, we need to know that if quantity inside |x-y| is greater than that inside |x-z| or not. now that is influenced by two factors.
i)the actual quantity of y and z
ii)the sign (+or-) of x,y and z.
this is because we do not know if x,y and z are integers or natural numbers or positive or negative. Genearally if x is common to x-y and x-z the answer depends on if Y > Z or not. say if X is 5 , Y is 3 and Z is 2, the answer could be found from statement 1 itself. But we have to take the negative sign too.
if X is -5 the result wud change. so A alone is insufficient.
if we take the second statement it says, in effect, x is negative. But wat abt Y and Z? so B alone is insufficient.
if we combine these, it is still insufficient as Y and Z may be positive or negative which will alter the final result significantly.
Hence E
hope this helps
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Re: Is |x – y| > |x – z|?  [#permalink]

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28 Jan 2014, 11:23
raghuraoram wrote:
Is |x – y| > |x – z|?

(1) |y| > |z|
(2) x < 0

I think that there is not a really quick way to solve this one but one can get in trouble if one tries to solve this algebraically.
I think this question calls for more of a conceptual approach, number line and stuff as Bunuel showed in his post

We are asked if the distance between X and Y is larger than that of X and Z

Both statements together won't do the trick, we can try cases by drawing a number line and trial and error

Just my 2cents
Cheers!
J
Manager
Joined: 07 May 2013
Posts: 93
Re: Is |x – y| > |x – z|?  [#permalink]

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05 Jun 2014, 00:35
Buneul, I think that you have made a mistake in interpreting |y|>|z|
====>|y|/|z|>1
====>either both are -ve or both are +ve.

----------z-----y----0-----------

Or

---------------------0-----z----y----
Math Expert
Joined: 02 Sep 2009
Posts: 55609
Re: Is |x – y| > |x – z|?  [#permalink]

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05 Jun 2014, 01:51
Buneul, I think that you have made a mistake in interpreting |y|>|z|
====>|y|/|z|>1
====>either both are -ve or both are +ve.

----------z-----y----0-----------

Or

---------------------0-----z----y----

No mistake there.

|y|>|z|, means y is farther from 0 than z, which gives us the following possible cases:

--y--------0---z--------
--y----z---0------------
-----------0---z------y--
------z---0-----------y--
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Re: Is |x – y| > |x – z|?  [#permalink]

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01 Nov 2016, 16:18
Is |x – y| > |x – z|?

(1) |y| > |z|
(2) x < 0

So I started by assuming x was negative. I had x=-2 y=-3 and z=-2
[-2-(-3)]>[-2-(-2)]
1>0 yes
then I tried x=-2, y=3, z=-2
[-2-3]>0
[-5]>0 yes
Then I tried setting y and z as positive
y=3, z=2
[2-3]>[2-2]
no
insuff

E
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Re: Is |x – y| > |x – z|?  [#permalink]

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28 Nov 2018, 01:07
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Re: Is |x – y| > |x – z|?   [#permalink] 28 Nov 2018, 01:07
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