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

the question is simply asking if the distance between x and y is larger than the distance between x and z.

statement 1:

y is further away from 0 than z is. we have no info on the position of x with relative to y and z. insufficient.

statement 2:

x < 0. no info on y and z. insufficient.

both statements together:

still insufficient since we do not know the relative position of x with respect to y and z. insufficient.

for eg.
if x = -1, y = -5, z = 2, then the answer to the question is YES.
if x = -4, y = -5, z = 2, then the answer to the question is NO.

choose E.

-BM-

apoorva.srivastva wrote:Is | x - y| > | x - z | ?

(1) | y | > | z |

(2) x < 0

1 is insufficient as we do not know the signs of y and z.
2 alone is insuffiecient as we do not have any information about y and z.
Taking 1 and 2 together we know that:
|x-y| = |-(k+y)| k+y (substituting -k for x) and |x-z| = |-(k+z)|= k+z
We still do not know the actual values of y and z in order to find which is greater.
Hence answer is C

plugging values..I am getting A

OA is E

I feel the best way to tackle such absolute value problems is using the number line and distance method.. It saves a lot of time.

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

You can rephrase the questions as is the distance between x and y greater than the distance between x and z

Statement 1: | y | > | z |

Here the value of x and hence its distance from y or z cannot be determined using this statement.

Statement 2: x<0

This statement just tells us that the value of x is negative and we cannot interpret the distance of y or z from x

Taking them together,

Consider this, if y and z are negative then the distance between x and z could be greater than the distance between x and y if x is closer to z or between z and 0.
Whereas distance between x and y could be greater than the distance between x and z if x is closer to y!!!

[Refer to the picture below to help you visualize this concept]

So since we have contradicting results we can conclude that neither of the statement are helpful. Hence the answer is E.