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If x, y and z are integers, is x – y greater than y – z?

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If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 27 Jan 2017, 08:37
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:34) correct 24% (02:35) wrong based on 99 sessions

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Re: If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 27 Jan 2017, 21:41
Compare x - y & y - z
1. x > z, we don't know about y
eg. x = 2, y = 3, z = 1 --> -1 < 2 but if x = 2, y = -3, z = 1 --> 5 > -4. Hence insuf
2. z > y --> y - z < 0. We're not sure x - y < 0 or > 0
Combine: x > z > y --> x - y > y - z
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Re: If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 28 Jan 2017, 03:22
x-y > y - z is equivalent to x+z > y + y
hence, claim 1 x > z is not sufficient as we don't know about how z relates to y, claim 2 z > y is not sufficient as we don't know about how x relates to y.
but claims 1 & 2 are jointly sufficient.
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Re: If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 28 Jan 2017, 10:52
1
Imagine this question as distance on the number line. So we need all 3 points.
So combining both statements,we get X>Z>Y. We found Z is lying between X and Y on number line.
So now we get X is far away from Y than Y is from Z. Hence Ans is C.
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If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 28 Jan 2017, 22:46
Hi,

it asks whether x-y>y-z ----> or x+z>2y ?

st1. states that x>z we can infer x+z>z+z with this we can rewrite question whether 2z>2y or simply z>y? as we don't know. insuff.

st2. it states z>y and we can rewrite the question whether x>y? no info therefore insuff.

st1+2. from 1 we arrive to whether z>y ? and 2 states that z>y therefore it is sufficient.
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Re: If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 26 Oct 2017, 13:29
rkvkvhariharan wrote:
Imagine this question as distance on the number line. So we need all 3 points.
So combining both statements,we get X>Z>Y. We found Z is lying between X and Y on number line.
So now we get X is far away from Y than Y is from Z. Hence Ans is C.



Loved your explanation. Even with -ve numbers the distance element remains the same
But just for my knowledge, if the stems said |x|> |z|and then |z| > |y|; would C still hold true?
Thank you!
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Re: If x, y and z are integers, is x – y greater than y – z?  [#permalink]

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New post 26 Oct 2017, 18:28
(1) x>z (no inf about y) [Clearly Insuff]
(2) z>y (no inf about x) [Clearly Insuff]

(1)&(2)

x............>z..................>y

Form the above number line, it is clear that x-y>y-z

Answer: C.
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Re: If x, y and z are integers, is x – y greater than y – z? &nbs [#permalink] 26 Oct 2017, 18:28
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