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# If x and y are consecutive negative integers, is x greater

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Manager
Joined: 20 Nov 2009
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If x and y are consecutive negative integers, is x greater  [#permalink]

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Updated on: 04 Aug 2010, 23:18
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Difficulty:

25% (medium)

Question Stats:

75% (01:28) correct 25% (01:47) wrong based on 113 sessions

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If x and y are consecutive negative integers, is x greater than y?

(1) x + 1 and y – 1 are consecutive negative integers.
(2) x is an even integer.

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But there’s something in me that just keeps going on. I think it has something to do with tomorrow, that there is always one, and that everything can change when it comes.
http://aimingformba.blogspot.com

Originally posted by aiming4mba on 04 Aug 2010, 22:58.
Last edited by aiming4mba on 04 Aug 2010, 23:18, edited 1 time in total.
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04 Aug 2010, 23:51
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aiming4mba wrote:
If x and y are consecutive negative integers, is x greater than y?
a. x + 1 and y – 1 are consecutive negative integers.
b. x is an even integer.

$$x$$ and $$y$$ are consecutive integers means that either:
$$y=x+1$$ (for example $$x=-5$$ and $$y=-4$$), in this case $$x<y$$;
OR:
$$x=y+1$$ (for example $$x=-5$$ and $$y=-6$$), in this case $$x>y$$.

So the we should determine which case we have.

(1) $$x+1$$ and $$y-1$$ are consecutive negative integers --> again either $$x+1=(y-1)+1$$ --> $$x+1=y$$ (first case so $$x<y$$) or $$y-1=(x+1)+1$$ --> $$y=x+3$$, which is not possible as $$x$$ and $$y$$ are consecutive integers (difference between two consecutive integers can not equal to 3). So only first case is possible: $$x<y$$. Sufficient.

(2) $$x$$ is an even integer. Clearly insufficient.

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Re: If x and y are consecutive negative integers, is x greater  [#permalink]

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20 Apr 2019, 03:37
Alternative approach: we can also translate the question into absolute equality.

given : |x-y| = 1

statement 1: |x+1-y+1| = 1
so |x+1-y+1| = |x-y|
if both sides have same sign, then x-y+2 = x-y; and 2 = 0 ---> invalid
if both sides have opposite signs, then x-y+2 = y-x ; and 2x + 2 = 2y ; and x+1 = y ---> so y is always greater than x by 1 ---> sufficient

statement 2: x is even ---> so y is odd but can still be smaller than or bigger than x by 1 ---> insufficient
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Re: If x and y are consecutive negative integers, is x greater   [#permalink] 20 Apr 2019, 03:37
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