Is |x-z| |x-y| ? (1) |z| |y| (2) 0 x

Question

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

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

Bunuel · Accepted Answer

"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.

gurpreetsingh · Answer

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 0z.

onedayill · Answer

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

Bunuel · Answer

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.

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

sumitsinha4u · Answer

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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