1. xyz < 0 means odd number of digits are negative in this case 1 or 3. No real information and hence not sufficient.
2. xy<0 means x and y are on opposite side of the number line . Hence x<0 & y> 0 or x>0 and y<0. This information is also not sufficient.

With 1 & 2 we have z > 0 as out of x and y only 1 is negative.
But we still don't know out of x,y which one is negative. So lets check both the options.

let x > 0 & y < 0 . In this case as z could be on either side of x and would still satisfy the condition that |x-z| < |x-y|. As this option itself yields 2 solution there is no need to check for other condition answer should be E.

ashforgmat wrote:153) Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0


[spoiler]Shudnt the answer be E for above? [/spoiler]

we can rephrase the question stem that x,y,and z must be positive or 2 of them must be negative

in statement o1, 1 or 3 variables could be negative so insufficient
in statement 02, here 1 variable must be negative, so insufficient

combined 1 or 3 variables could be negative so insufficient


correct me if my reasoning is wrong

Hey I arrived to (E). Just wanted to post the way I solved it.

|x - y| > |x - z|; Is x < z < y ? OR y < z < x ?

Find the positive ABS:
x - y > x - z
-y > -z
y < z

STMT 1: Insufficient
x y z < 0
+ + - < 0
+ - + < 0
- + + < 0

STMT 2: Insufficient
x y < 0
+ - < 0
- + < 0

Combined 1 & 2, only these two scenerios are posible:
x y z < 0
+ - + < 0
- + + < 0

But from the positive ABS we know that y < z, so y must be negative and z positive so the only possible sceneario is:
x y z < 0
+ - + < 0

So it turns out that y < z ? x. If we look at |x - y| > |x - z| the value of x could equal z, but there's no way to confirm that.

So picked (E)!!!

Just saw so many lengthy replies on the previous page.
We should simply take few values and solve this question
It can be done in 1:30 mins approx
From statement 1 we know that either one out of x,y,or z is negative or all three are negative
Hence we cannot find out the answer
From second statement we cannot find put any information about z
Hence, insufficient
Even after using both the statements together we cannot find the answer
Hence, E

E:

(1) either all three should be negative or one of them:
x=-2
y=-4
z=-3 or -1 => Insuficient

(2) either x or y should be negative. z can be before and after x

(1+2)
tells that z is positive but no restrictions for z to be on the line between x and y

Testluv wrote:I'd say about 640-660!

I don't know, I think it's about as hard as absolute value and inequalities can get, IMO. 700+. Seriously, most people it would take 5 minutes to figure out, or most would guess.

Testluv wrote:I'd say about 640-660!

How do you identify the score with a question?? This is a question just out of curiosity.

I know the ANSWER is NOT E but ...?

i am still not able o get this question how the answer choice E is correct

prashant misra wrote:i am still not able o get this question how the answer choice E is correct

Pasting the question again --

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


SOLUTION: --

statement 1--

product of xyz is less than zero

this implies either 1 of them or all of them are negative


Suppose only 1 of them is negative (say z)

let's choose values -- Z= -1

X= 0
Y = 5

this fulfills the condition ..

Distance between XY (5) is greater than distance between XZ (1)

Here Z is not present between X and Y.

Now suppose all of them are negative

X= -1
Y = -5
z= -2

In this case as well the condition given in the question is fulfilled.

But, here Z lies betwen X and Y.

Hence Statement 1 is INSUFFICIENT


Statement 2 --

Product of XY is less than zero

nothing is given about Z .. So Z can be anything (NEGATIVE or POSITIVE) -- Hence, we cannot conclude anything about Z's position.

Hence Statement 2 is INSUFFICIENT


Now let's combine the 2 conditions..

we have XY <0 [mean either X or Y is NEGATIVE) and xyz < 0 [ Since we know that either X or Y is negative and the whole product is also negative , Z is POSITIVE)

(I hope this point is clear to you)

let's assign some values

X = -1
Y = 4
Z = 2

This satisfies the condition [ distance between XY (5) is greater than distance between XZ (3)] -- here Z is between X and Y

now say Z is negative

X = 1
Y = 10
Z = -2

This also Satisfies the condition [ distance between XY (9) is greater than distance between XZ (3)] -- Here Z is NOT between X and Y


Therefore, even the two statments combined cannot give us any unique answer.

CORRECT ANSWER = E

Deependra1 wrote:I know the ANSWER is NOT E but ...?

E is the correct answer!

saketk wrote:

prashant misra wrote:i am still not able o get this question how the answer choice E is correct

Pasting the question again --

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

Here is another solution:

Plug in numbers:
a. xyz<0
x=-1, y=0, z=1 - False
x=1, y=0, z=-1 - False
x=1, y=-1, z=0 - True

Not sufficient - No A&D

b.xy<0
No info on Z, so we cannot conclude since the sign of z (+ or -) can decide the result.- No B

Now, C or E?

C? - Together xyz<0 and xy<0, now we know Z is positive and greater than zero
Again plugin the first set with positive z value alone
x=-1, y=0, z=1 - False
x=2, y=0, z=1 - True

Still both results are possible, so insufficient.

So choose E. Hope it helps. It's about two minutes to plugin and find out.

very tricky ...
E

E!!