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Difficulty:
25%
(medium)
Question Stats:
75% (01:35) correct
25%
(02:14)
wrong
based on 119
sessions
History
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Not Attempted Yet
If x, y and z are integers, is x – y greater than y – z?
(1) x > z
(2) z > y
_________________
(1) x > z
(2) z > y
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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GMAT 1: 540 Q45 V20
Posts: 5
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
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
Posts: 29
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.
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.
rkvkvhariharan
Joined: 09 Jun 2015
Last visit: 28 Mar 2017
Posts: 7
Concentration: Entrepreneurship, Finance
Schools: HBS '18 Stanford '18 Booth '18 Sloan '18
Schools: HBS '18 Stanford '18 Booth '18 Sloan '18
Posts: 7
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.
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.
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
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
Posts: 249
rkvkvhariharan
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!
(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.
(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.
RahulJain293
Joined: 24 Apr 2022
Last visit: 13 Sep 2026
Posts: 162
Location: India
Concentration: General Management, Nonprofit
GMAT Focus 1: 585 Q81 V80 DI76 
GMAT Focus 1: 585 Q81 V80 DI76
Posts: 162
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?
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?
RahulJain293
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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RahulJain293
Joined: 24 Apr 2022
Last visit: 13 Sep 2026
Posts: 162
Location: India
Concentration: General Management, Nonprofit
GMAT Focus 1: 585 Q81 V80 DI76
GMAT Focus 1: 585 Q81 V80 DI76
Posts: 162
Bunuel
Ugh! My bad! Thanks a lot
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