On a number line if x y is z between x and y? (1) x z

Question

On a number line if x > y, is z between x and y?

(1) x < 0
(2) y - x > z

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chetan2u · Answer

Clearly both are insufficient individually. 
1) x<0
y and z could be anything. 
x=-1, y=-5 and z=-2....yes
x=-1, y=-2 and z=-5....no

2) y-x>z.....y>x+z
So x>y>x+z
x=-1, y=-5 and z=-4.5....yes
x=-1, y=-5 and z=-6.......no

Combined we get 0>x>y>x+z
The examples of statement (2) still stand
Insuff

E

catinabox · Answer

I wonder if there is a typo on the question?

"On a number line is x > y, is z between x and y?"
Was it supposed to be: "On a number line   if   x > y, is z between x and y?"

RaghavKhanna · Answer

Bunuel  sir,
Is there a typo in this question? Shouldn't it be: if x > y, is y - x > z?

GMATGuruNY · Answer

I assume that the prompt should read as follows:

Statement 1:
No information about z.
INSUFFICIENT.

Statement 2: 
Adding together x>y and y-x>z, we get:
x+y-x>y+z
y>y+z
0>z
z<0

Let z=-10, implying that y-x>-10.
Case 1: y=-10 and x=-1, with the result that y-x=-9.
In this case, z is NOT between x and y, so the answer to the question stem is NO.
Case 2: y=-11 and x=-2, with the result that y-x=-9
In this case, z IS between x and y, so the answer to the question stem is YES.

Case 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

E

Bunuel · Answer

Yes. Edited the typo. Thank you.

On a number line if x > y is z between x and y? (1) x < 0 (2) y - x >z

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