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I think we need to develop intuition for these kind of questions... from looking at question i was not able to say the answer but after looking at choices, i started to feel it must be E. After less then a minute of thinking i was sure it has to be E.

It is E. We can make out pretty quickly that these are heavily based on values of X, Y, and Z. So it has to be C or E. You are subtracting Y and Z from a fixed value of X. Having absolute values is not going to help. Nice post but! Thanks.

Re: Is |x - y|>|x - z|? [#permalink]
25 Aug 2010, 07:14

1

This post received KUDOS

In general for these types of questions, if I'm testing values, are the variables different from each other.. eg should I consider the case where x = y, or x = z unless otherwise stated?

Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
22 May 2012, 19:20

1

This post received KUDOS

I used the approach below :

1) |y|>|z| will give 4 different cases , I assumed only two y=5 , z=2 & y=-5 , z= -2 No information about x , so x can be =+ ve or -ve , let x = 7 x-y=7-5 =2& x-z= 7-2=5

First, remember what do we use the absolute value for ? We use it to express the distance between two real numbers on the number line. So, |x - y| means the distance between x and y, and |x| = |x - 0| means the distance between x and 0. Also, |x + 3| = |x - (-3)| expresses the distance between x and -3. Obviously, |x - y| = |y - x| (it is the same distance).

So, the question can be rephrased as "is the distance between x and y greater that the distance between x and z ?" or "is x closer to z than to y?"

(1) |y| > |z| means that the distance from y to 0 is greater than the distance from z to 0. This in fact is not important in this case. But certainly y and z are distinct. Regardless of wheather y > z or y < z (both cases are possible, try to draw the number line and visualize the points), we can place x closer to either y or z. So, (1) is not sufficient.

(2) Is evidently not sufficient. Take a point x on the number line at the left of 0, then you can place y and z as you please, each one can be closer or farther from x. Also, now you can consider y = z, in which case the two distances are equal.

Evidently, considering (1) and (2) together won't help either. For example, put x at the left of 0, y and z on either side of x such that y < x and z > x, both negative. You can play with each distance and put either y or z closer to x.

Therefore, answer, E. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

1. |z| > |y| \(z^2>y^2\) \(z^2-y^2>0=y^2-z^2<0=(y-z)(y+z)<0\) So one between (y-z) (y+z) is negative, the other is positive, but we cannot tell which one is +ve or -ve. \(2x(y-z)>(y+z)(y-z)\) the second part is -ve ((y-z)(y+z)<0) we cannot say anything about 2x(y-z) Not sufficient

2. 0 > x x<0 so the first term is -ve (2x) but we cannot say anything about the other part (...(y-z)>(y+z)(y-z))

(1)+(2) Still not sufficient, let me explain. Here are the combinations ( remeber that one between (y-z) (y+z) is negative and the other positive) \(2x(y-z)>(y+z)(y-z)\) Case one (y-z)-ve: 2x<0 (y-z)<0 (y+z)>0 -veNumber*-veNumber>+veNumber*-veNumber +ve>-ve always true. Case two (y+z)-ve: 2x<0 (y-z)>0 (y+z)<0 -veNumber*+veNumber>-veNumber*+veNumber -veNumber>-veNumber we cannot say if this is true, since we have no numerical value

E

Do I deserve a Kudos for this? _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Is |x - y|>|x - z|? [#permalink]
25 Aug 2010, 07:28

Expert's post

krazo wrote:

In general for these types of questions, if I'm testing values, are the variables different from each other.. eg should I consider the case where x = y, or x = z unless otherwise stated?

Sorry if this is a dumb question.. lol

Unless otherwise specified, variables could represent the same number. _________________

Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
22 May 2012, 17:06

try assuming values y=3 z=2 ... x can be any no. +ve / -ve (take both cases to decide between A & C) but eventualy both did not give answer so E is correct

gmatclubot

Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0
[#permalink]
22 May 2012, 17:06

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