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Math Expert V
Joined: 02 Aug 2009
Posts: 7952
If x=y+1 and x is a non-negative integer, is x even?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 51% (01:33) correct 49% (01:52) wrong based on 70 sessions

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If $$x=y+1$$ and $$x$$ is a non-negative integer, is x even?

(1) $$y^2 +1$$ is even.
(2) $$y$$ is a negative integer.

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Joined: 05 Feb 2017
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Re: If x=y+1 and x is a non-negative integer, is x even?  [#permalink]

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1
Given X is a non negative integer and x=y+1 so y has to be an integer.

St:1 From this we can deduce that y is odd because odd+1 is even.
And if y is odd x will be even.
Sufficient.

St:2 Given y is a negative integer and also in question stem it is given that x should be a non negative integer. So only y=-1 satisfies
For this X will be 0 and hence even.
Sufficient

IMO D

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Joined: 15 Oct 2017
Posts: 295
GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39 Re: If x=y+1 and x is a non-negative integer, is x even?  [#permalink]

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From 1: O + O= E
Therefore, y = O & X = O+O = Even
Sufficient

From 2: The only possible negative integer value of y for x to be non-negative integer given that x=y+1 is -1.
Therefore, x=-1+1=0, Even
Sufficient

IMO D
Retired Moderator V
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If x=y+1 and x is a non-negative integer, is x even?  [#permalink]

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If x=y+1 and x is a non-negative integer, is x even?

(1) y^2 + 1 is even.
According to this statement, we get y ^2 is odd. now y can't be non-integer as, x = y+1 is an integer.
So, y is an odd integer (-ve or +ve integer). So, x = y+1 = odd+odd = even.
Hence, it is sufficient.
P.S, it doesn't matter whether y is -ve or +ve, eg. -1+1 = 0 (even) . 3+1 = 4 (even)
(2) y is a negative integer.
now, y is -1, x = 0 even, if y is any other integer other than -1, then x would be negative... hence it will dissatisy the question stem, which is not possible.
Hence x = 0, even
It is sufficient.
_________________ If x=y+1 and x is a non-negative integer, is x even?   [#permalink] 26 Jan 2018, 07:21
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