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

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Is |x-z| > |x-y| ? [#permalink]

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New post 14 Jul 2010, 10:18
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Is |x-z| > |x-y| ?

(1) |z| > |y|
(2) 0 > x
[Reveal] Spoiler: OA

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Re: Inequality problem DS [#permalink]

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New post 14 Jul 2010, 10:54
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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New post 14 Jul 2010, 11:17
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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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New post 14 Jul 2010, 19:25
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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 .... :oops:
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Re: Inequality problem DS [#permalink]

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New post 14 Jul 2010, 19:39
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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 .... :oops:


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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Is |x-z| > |x-y| ? [#permalink]

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Is |x - z| > |x - y|? [#permalink]

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New post 04 Feb 2015, 05:11
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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New post 04 Feb 2015, 05:18
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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New post 04 Feb 2015, 11:39
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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:
[Reveal] Spoiler:
E


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Is |x – z| > |x – y|? [#permalink]

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New post 15 Aug 2015, 07:12
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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New post 15 Aug 2015, 08:20
can anyone answer this
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Re: Is |x – z| > |x – y|? [#permalink]

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New post 15 Aug 2015, 08:25
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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New post 15 Aug 2015, 08:25
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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New post 01 Oct 2015, 11:59
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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New post 24 May 2017, 08:19
Hello from the GMAT Club BumpBot!

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Re: Is |x-z| > |x-y| ?   [#permalink] 24 May 2017, 08:19
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