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

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Bunuel
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If x, y and z are integers, is x – y greater than y – z? [#permalink] New post   27 Jan 2017, 09:37
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A
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C
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E

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74% (01:34) correct 26% (02:14) wrong based on 116 sessions
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If x, y and z are integers, is x – y greater than y – z?

(1) x > z
(2) z > y
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C
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rkvkvhariharan
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Re: If x, y and z are integers, is x – y greater than y – z? [#permalink] New post   28 Jan 2017, 11:52
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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] New post   05 Jan 2023, 09:24
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RahulJain293 wrote:
Hi All,

I have a doubt here. When I pick values as x = -1, y = -2, z = -3, and it satisfies x > y > z i.e -1 > -2 > -3

But when we try x- y - we'd get -1 - (-2) = -1 + 2 = 1
and y-z we'd get -2 - (-3) = -2 + 3 = 1

in this case, we get both as equal.. Where am I going wrong?? bb or Bunuel ? any help here?


It's given that x > z > y, not x > y > z.

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

Is x – y > y – z ?
Is x + z > 2y

(1) x > z. No info about y. Not sufficient
(2) z > y. No info about x. Not sufficient

(1)+(2) Sum the above: x + z > z + y. Since z > y, then x + z > z + y > y + y. Thus, x + z > z + y > 2y. SWufficient.

Answer: C.

Hope it's clear.
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Re: If x, y and z are integers, is x – y greater than y – z? [#permalink] New post   27 Jan 2017, 22:41
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] New post   28 Jan 2017, 04:22
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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If x, y and z are integers, is x – y greater than y – z? [#permalink] New post   28 Jan 2017, 23:46
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.
C
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Re: If x, y and z are integers, is x – y greater than y – z? [#permalink] New post   26 Oct 2017, 14:29
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] New post   26 Oct 2017, 19:28
(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? [#permalink] New post   05 Jan 2023, 09:03
Hi All,

I have a doubt here. When I pick values as x = -1, y = -2, z = -3, and it satisfies x > y > z i.e -1 > -2 > -3

But when we try x- y - we'd get -1 - (-2) = -1 + 2 = 1
and y-z we'd get -2 - (-3) = -2 + 3 = 1

in this case, we get both as equal.. Where am I going wrong?? bb or Bunuel ? any help here?
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RahulJain293
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Re: If x, y and z are integers, is x y greater than y z? [#permalink] New post   05 Jan 2023, 09:35
Bunuel wrote:
RahulJain293 wrote:
Hi All,

I have a doubt here. When I pick values as x = -1, y = -2, z = -3, and it satisfies x > y > z i.e -1 > -2 > -3

But when we try x- y - we'd get -1 - (-2) = -1 + 2 = 1
and y-z we'd get -2 - (-3) = -2 + 3 = 1

in this case, we get both as equal.. Where am I going wrong?? bb or Bunuel ? any help here?


It's given that x > z > y, not x > y > z.

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

Is x – y > y – z ?
Is x + z > 2y

(1) x > z. No info about y. Not sufficient
(2) z > y. No info about z. Not sufficient

(1)+(2) Sum the above: x + z > z + y. Since z > y, then x + z > z + y > y + y. Thus, x + z > z + y > 2y. SWufficient.

Answer: C.

Hope it's clear.


Ugh! My bad! Thanks a lot :)
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Re: If x, y and z are integers, is x y greater than y z? [#permalink]
05 Jan 2023, 09:35
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Bunuel
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