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Complex absolute value question

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Source: — Data Sufficiency |
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by UmanG » Sun Aug 05, 2007 9:44 pm
Hi,

My answer is B. Explaination is as follow,

1. Y < X,

Here if both X & Y holds the same sign either positive or negative will change the above equation to |X-Y| = |X| - |Y|

And if both have oppsite signs then since Y < X it holds the equation,
|X-Y| > |X| - |Y|

It means this option gives us |X-Y| >= |X| - |Y|.

Stetement 1 alone is NOT SUFFICIENT.

2. XY<0

This equation tells us that X & Y has oppsite signs.

Now for +ve X & -ve Y
|X-(-Y)| > |X| - |(-Y)|
--> |X+Y| > |X| - |Y|-----------(A)
(clearly X+Y in either condition will grater then X-Y.)

Or for -ve X & +ve Y
|(-X)-Y| > |(-X)| - |Y|
--> |-X-Y| > |X| - |Y|
--> |X+Y| > |X| - |Y|-----------(B)
(Same as A)

Thus using stetement 2, in either condition (+ve X & -ve Y, -ve X & +ve Y)we clearly able to say that |X-Y| > |X| - |Y|.

And so stetement 2 alone is SUFFICIENT.
Thanks,
UmanG - restless mind..
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by mbaapp07 » Mon Aug 06, 2007 10:14 am
Uman is absolutely right...
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by singhpreet1 » Fri Jun 11, 2010 10:49 pm
cant understand the solution..i felt A alone was sufficient..would someone probe into this..or is it too old a problem to be looked into!??
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by Haaress » Wed Jun 16, 2010 2:26 pm
|X-Y| > |X| - |Y|

1. Y < X

Plug ins works well with this one.
|X-Y| > |X| - |Y|
3 cases.
X is +ve and Y is +ve eg |5-2| > |5| - |2| .. No
X is +ve and Y is -ve eg |5-(-2)| > |5| - |-2| ... Yes
X is -ve and Y is -ve eg |-2-(-5)| > |-2| - |-5|...Yes

So Insufficient

2. XY<0

2 Cases
X is +ve and Y is -ve eg |5-(-2)| > |5| - |-2| ... Yes
X is -ve and Y is +ve eg |-5 - 2| > |-5| - | 2| ... Yes

So sufficient. Thus B.
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by mj78ind » Fri Jun 18, 2010 6:34 am
UmanG wrote:Hi,


2. XY<0

This equation tells us that X & Y has oppsite signs.

Now for +ve X & -ve Y
|X-(-Y)| > |X| - |(-Y)|
--> |X+Y| > |X| - |Y|-----------(A)
(clearly X+Y in either condition will grater then X-Y.)

Or for -ve X & +ve Y
|(-X)-Y| > |(-X)| - |Y|
--> |-X-Y| > |X| - |Y|
--> |X+Y| > |X| - |Y|-----------(B)
(Same as A)

Thus using stetement 2, in either condition (+ve X & -ve Y, -ve X & +ve Y)we clearly able to say that |X-Y| > |X| - |Y|.

And so stetement 2 alone is SUFFICIENT.
Slight modification, if y <0, then abs(x-y) = abs(x) + abs(y) ......which is always greater than abs(x) - abs(y)
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