both condition should meet to answer this question.

There are only two conditions which need to be analyzed for this question.
1) when x & y are different signs.
2) z is either positive or negative.
Additional condition is z is closer to x than y is.

So, when xyz -> + - +, then the way the numbers line up on the number line could be yxz or yzx. So, thats insufficient. Z may or may not be in the centre.
Likewise, when xyz -> - + +, then the way the three integers line up could be xyz or xzy. So, thats insufficient as well. Z may or may not be in the centre.

But notice the value of z is not constrained by any given information so z can technically be extreme negative or extreme positive and still satisfy conditions 1) and 2) while x & y are opp signs.

Therefore, E.

Definitely E....
We cant infer the position of Z on no. line from given options

straight (E)
(b) doesnt say anythng abt Z and (a) says that either one or all the three are negative nos.
which is insufficient.combing both will lead us to insufficient details to answer.

1) not sufficient! clearly indicates x, y and z could be in any order on the number line

2) tricky! coz z value is not mentioned. it could take a positive value closer to x than y or a negative value closer to x than y.
not sufficient!

E

E in answEr.

For some reason the web site and the email through which I received the question do not show the multiple choice answers.. In any case my thinking is that thee isnt enough data to answer the question. Y Z or both could be negative numbers and because of that you dont know enough about either relative position as a negative number to complete the task. So whatever answer relates to that I hope wins.

On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
a) xyz < 0
b) xy < 0

When no order is specified, consider different -- especially non-alphabetic -- orderings of the given points.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..................z=9.....x=10
Here, z lies between x and y.

The following case satisfies all of the constraints in the problem:
y=-10..............................0..............................x=10....z=11
Here, z does NOT lie between x and y.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

I) xy<0
Arrangement options: xz0y,zx0y,x0zy,xoyz,...
INSUFFICIENT

II) xyz<0
Arrangement options: x0zy,x0yz,xz0y, zx0y,...
INSUFFICIENT

COMBINED:
Arrangement options: x0zy,x0yz, ...
INSUFFICIENT
]

E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

fundamentals are important so i have solved the number-line question with number line and thanks for the question.

Given line segment xy>xz so they can be placed on number line in aforesaid way.
Now if we put relative positions of zero only following inference can be concluded with certainty.

That there would be only 2 definite cases where z cannot fall between x and y.
In rest of the cases we need more info to determine the positions.
Case1 x and y negative and z positive
Case 2 x and y positive and z negative
Concluding "z" can't fall between "x" and "y" if "x" and "y" have same sign and z opposite.

Statement 1
xyz<0, chances are xy and z may be of opposite sign or same sign so it's insufficient.

Statement 2
xy<0, xy are of opposite sign but no info on z sign so it's insufficient

Combining
z>0 and x and y have opposite sign again no definite conclusion.

So ans is E

x distance to y > x distance to z
A) xyz< 0
either 1 are negative
y,0,z,x
y,0,x,z
x,0,z,y
x,0,y,z


or All three are negative
y,z,x,0
y,x,z,0
x,z,y,0
x,y,z,0

B) xy < 0

1) x <0 & y >0
x 0 z y
z x 0 y
x z 0 y
2) x>0 & y<0
y z 0 x
y 0 z x
y 0 x z

B is Insufficient

Answer is E

Chose E

E