x, y, z are numbers on the number line. Is x

Question

x, y, z are numbers on the number line. Is x < y < z ?

a) |y-x| + |y-z| = |z-x|

b) x<z

kook44 · Answer

Here's my shot: for the record, number property data sufficiencies, ESPECIALLY inequalities and and absolute value (this one has both :shock:

) are my achillies heel a) |y-x| + |y-z| = |z-x| this tells us that the distance on the number line between z and x is greater than that of both y and x, and y and z. so z is farther from x than it is from y, and since the distance between z and x is greater than y and x, y MUST be between z and x, but we dont know if x

Matador · Answer

Agree. C is the answer.

Elaborating on kook44's answer, if we pick numbers:

Stmt 1:

We know that y has to be in the middle (see kook44's explanation). Therefore,

If x = -2 and z = 4, then y = 1 (it has to be the middle point in order for the equation to hold), we are given

x < y < z
-2 < 1 < 4 ---> Stmt 1 proves that x < y < z.

However, even though y has to be the middle number, we do not know which one of x and z is the greatest number. Therefore, the reverse could be the case:

x > y > z
4 > 1 > -2 ---> Stmt 1 one is insufficient.

Stmt 2:

Says nothing about y. Insufficient.

Stmt 1 + 2:

x < z , therefore, only this can be true:

x < y < z
-2 < 1 < 4 ---> Yes, x < y < z is true.

Answer, C.

vivek123 · Answer

I'm taking "E" on this.

it can be y=x, then answer is NO
if y & x are different numbers, answer is YES.

I considered y = x case since it is not given that the numbers are different. Laxie, can I consider this? :shock:

chuckle · Answer

I am for C. 
But, I think vivek pointed out right - what if x=y or y=z?

laxieqv · Answer

Good point, buddy!! :wink:

And congrat to you, OA is E

joemama142000 · Answer

how can x=y?

the q stem says x<y<z

laxieqv · Answer

it's the question, buddy :wink:

ccax · Answer

Any triples of {x,y,z} where x=y OR y=z will
satisfy (1) and (2), but it is NOT x<y<z.

A few triples that satisfy (1) and (2) and where x<y<z are:
{x,y,z}
{-1,0,1}
{0,1,2}
{0,1,3}
{2,3,4}
{2,3,5}

A few triples that satisfy the (1) and (2) and where NOT x<y<z are:
{x,y,z}
{1,3,3}
{2,2,4}
{3,3,4}
{3,3,5}
{4,5,5}

x, y, z are numbers on the number line. Is x < y < z ?

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