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# Is |x-z| > |x-y| ?

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Retired Moderator
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Is |x-z| > |x-y| ? [#permalink]

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14 Jul 2010, 11:18
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45% (medium)

Question Stats:

59% (01:29) correct 41% (01:07) wrong based on 367 sessions

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Is |x-z| > |x-y| ?

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

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Re: Inequality problem DS [#permalink]

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14 Jul 2010, 11:54
Hussain15 wrote:
Is $$|x-z| > |x-y|$$ ?

1. $$|z| > |y|$$
2. $$0 > x$$

IMO C
|x-z| means distance between point x and z on number line
|x-y| means distance between point x and y on number line
thus overall question is simply asking whether x is closer to z or y

Statement 1 means
-z , -y , 0 , y , z these are the points in the order on the number line.
if x <0 then answer is yes , if x >z the answer is no thus not sufficient.

Statement 2 is not sufficient as it does not talk about z and y

now if you combine both of them...x<0 then it will be always closer to y than z. Thus both taken together are sufficient. Hence C

But since your answer is E....this is possible if 2nd statement is x>0 rather than x<0
as for x >0 ..the answer to the question is yes for 0<x<y and no for x>z.
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Re: Inequality problem DS [#permalink]

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14 Jul 2010, 12:17
2
2
Hussain15 wrote:
Is $$|x-z| > |x-y|$$ ?

1. $$|z| > |y|$$
2. $$0 > x$$

"Is $$|x-z|>|x-y|$$", means is the distance between $$x$$ and $$z$$ more than the distance between $$x$$ and $$y$$.

The best way would be just to draw the number line and consider several examples:

------x------0--y------z- satisfies both statements and the answer to the question is YES (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=12$$);

--z--x------0--y-------- satisfies both statements and the answer to the question is NO (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=-12$$).

Answer: E.

Hope it's clear.
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Re: Inequality problem DS [#permalink]

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14 Jul 2010, 20:25
1
Bunuel wrote:
Hussain15 wrote:
Is $$|x-z| > |x-y|$$ ?

1. $$|z| > |y|$$
2. $$0 > x$$

"Is $$|x-z|>|x-y|$$", means is the distance between $$x$$ and $$z$$ more than the distance between $$x$$ and $$y$$.

The best way would be just to draw the number line and consider several examples:

------x------0--y------z- satisfies both statements and the answer to the question is YES (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=12$$);

--z--x------0--y-------- satisfies both statements and the answer to the question is NO (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=-12$$).

Answer: E.

Hope it's clear.

Can you please explain again.
unable to understand ....
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Re: Inequality problem DS [#permalink]

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14 Jul 2010, 20:39
onedayill wrote:
Bunuel wrote:
Hussain15 wrote:
Is $$|x-z| > |x-y|$$ ?

1. $$|z| > |y|$$
2. $$0 > x$$

"Is $$|x-z|>|x-y|$$", means is the distance between $$x$$ and $$z$$ more than the distance between $$x$$ and $$y$$.

The best way would be just to draw the number line and consider several examples:

------x------0--y------z- satisfies both statements and the answer to the question is YES (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=12$$);

--z--x------0--y-------- satisfies both statements and the answer to the question is NO (or consider the following numbers: $$x=-10$$, $$y=2$$ and $$z=-12$$).

Answer: E.

Hope it's clear.

Can you please explain again.
unable to understand ....

Can you please specify what part didn't you understand?

2 number lines represent possible position of the numbers $$x$$, $$y$$ and $$z$$ on them, these positioning satisfy both statement 1 and 2 and give different answer to the question "is the distance between $$x$$ and $$z$$ more than the distance between $$x$$ and $$y$$" thus statenment taken together are not sufficient: answer E.

Also possible values of $$x$$, $$y$$ and $$z$$ are given (which also satisfy both statement 1 and 2). If you condsider these examples you'll see that the answer to the question "is $$|x-z|>|x-y|$$" will be in one case YES and in another NO. Two different answers, hence not sufficient.
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Is |x - z| > |x - y|? [#permalink]

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04 Feb 2015, 06:11
Is $$|x - z| > |x - y|$$ ?

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

Could someone please explain the answer to this question. Thanks
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Re: Is |x - z| > |x - y|? [#permalink]

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04 Feb 2015, 06:18
kdatt1991 wrote:
Is $$|x - z| > |x - y|$$ ?

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

Could someone please explain the answer to this question. Thanks

Actually it's fine... I have found the answer to this question on another forum:

http://gmatclub.com/forum/is-x-z-x-y-97235.html?fl=similar

http://gmatclub.com/forum/is-x-y-x-z-88818.html?fl=similar
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Re: Is |x-z| > |x-y| ? [#permalink]

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04 Feb 2015, 12:39
1
Hi All,

This DS question can be solved by TESTing VALUES. You'll have to be thorough with your thinking though (the absolute value signs *hint* that you'll need to consider 0 and negative values as part of your work).

We're asked if |X-Z| > |X-Y|. This is a YES/NO question.

Fact 1: |Z| >|Y|

Since there's no mention of X, you might instinctively think that this is insufficient, but here's the PROOF:

IF...
X = 1
Y = 0
Z = 1
|1-1| is NOT > |1-0| so the answer to the question is NO.

IF...
X = -1
Y = 0
Z = 1
|-1-1| IS > |-1-0| so the answer to the question is YES.

Fact 2: 0 > X

This Fact doesn't mention Y or Z, so you might also instinctively think that this is insufficient, but here's the PROOF:

IF...
X = -1
Y = 0
Z = 1
|-1-1| IS > |-1-0| so the answer to the question is YES.

IF...
X = -1
Y = 0
Z = -2
Then |-1-(-2)| is NOT > |-1-0| so the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we know...
|Z| > |Y|
0 > X

Thankfully, we already have all of the proof that we need (in the above examples)...
IF...
X = -1
Y = 0
Z = 1
|-1-1| IS > |-1-0| so the answer to the question is YES.

IF...
X = -1
Y = 0
Z = -2
Then |-1-(-2)| is NOT > |-1-0| so the answer to the question is NO.
Combined, INSUFFICIENT.

Final Answer:

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Is |x – z| > |x – y|? [#permalink]

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15 Aug 2015, 08:12
Is |x – z| > |x – y|?

(1) |z| > |y|
(2) 0 > x
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Re: Is |x – z| > |x – y|? [#permalink]

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15 Aug 2015, 09:20
can anyone answer this
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Re: Is |x – z| > |x – y|? [#permalink]

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15 Aug 2015, 09:25
Mascarfi wrote:
Is |x – z| > |x – y|?

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

Hello @
Here this topic was discussed.
is-x-z-x-y-97235.html?fl=similar

Please use search before posting.
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Is |x – z| > |x – y|? [#permalink]

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15 Aug 2015, 09:25
This topic have been merged with: http://gmatclub.com/forum/topic-97235.html
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Is |x-z| > |x-y| ? [#permalink]

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01 Oct 2015, 12:59
E is the correct answer.

Let us consider the following value :-

x z y |x-z| |x-y| |x-z|>|x-y|
3 2 1 1 2 NO
3 -2 -1 5 4 YES
-3 2 1 5 4 YES
-3 -2 -1 1 2 NO

For statement 1. |z| > |x| --> We are getting Yes and NO. Which implies that this statement is insufficient.
And for Statement 2. 0>x --> Which activate x's two value (-3 ), which again don't satisfy, as they are giving two value.
Now when you combine --> Which again give two value
x z y |x-z|>|x-y|
-3 2 1 YES
-3 -1 -2 NO.

Hope this answer your query
Sumit kumar
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Re: Is |x-z| > |x-y| ? [#permalink]

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24 May 2017, 09:19
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Re: Is |x-z| > |x-y| ?   [#permalink] 24 May 2017, 09:19
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