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# If x and y are integers, which of the following must be an even intege

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Math Expert
Joined: 02 Sep 2009
Posts: 58327
If x and y are integers, which of the following must be an even intege  [#permalink]

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12 Mar 2018, 21:46
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If x and y are integers, which of the following must be an even integer?

A. x + y
B. x + y + 1
C. 2xy + 1
D. 2xy + 2
E. 2x/y

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Math Expert
Joined: 02 Sep 2009
Posts: 58327
Re: If x and y are integers, which of the following must be an even intege  [#permalink]

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12 Mar 2018, 21:50
Intern
Joined: 18 Jul 2016
Posts: 35
Re: If x and y are integers, which of the following must be an even intege  [#permalink]

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12 Mar 2018, 22:07
IMO D

A)
when both x,y = even/odd ; x + y = even
when x =even, y = odd ; x+ y = odd
when x =odd, y = even; x+ y = odd
B)
when x+ y = odd; x + y+ 1 = even
when x+ y = even ; x + y+ 1 = odd

C) 2xy + 1 => 2xy --always even + 1 = odd

D) 2xy + 2 = even + even = even => answer

E) 2x/y => result may or may not be an integer
Manager
Joined: 01 Feb 2017
Posts: 243
Re: If x and y are integers, which of the following must be an even intege  [#permalink]

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13 Mar 2018, 11:57
Ans D

X and y are integers

xy- An Integer
2xy- Even Integer
2xy + 2- Even + Even- Even Integer

Posted from my mobile device
VP
Joined: 07 Dec 2014
Posts: 1222
If x and y are integers, which of the following must be an even intege  [#permalink]

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13 Mar 2018, 18:35
Bunuel wrote:
If x and y are integers, which of the following must be an even integer?

A. x + y
B. x + y + 1
C. 2xy + 1
D. 2xy + 2
E. 2x/y

2xy+2=2(xy+1)
as a multiple of 2, it must be even
D
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Re: If x and y are integers, which of the following must be an even intege  [#permalink]

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15 Mar 2018, 10:14
Bunuel wrote:
If x and y are integers, which of the following must be an even integer?

A. x + y
B. x + y + 1
C. 2xy + 1
D. 2xy + 2
E. 2x/y

Since even + even = even, and since 2xy and 2 are even, 2xy + 2 = even.

Answer: D
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Joined: 14 Jan 2018
Posts: 18
Re: If x and y are integers, which of the following must be an even intege  [#permalink]

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18 Mar 2018, 21:40
Bunuel wrote:
If x and y are integers, which of the following must be an even integer?

A. x + y
B. x + y + 1
C. 2xy + 1
D. 2xy + 2
E. 2x/y

IMO D
Even Number: 2*anything
Odd number: 2*n + 1
D: (2xy+2)----> 2(xy+1)---->2*anything. so D is the answer
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Re: If x and y are integers, which of the following must be an even intege   [#permalink] 18 Mar 2018, 21:40
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# If x and y are integers, which of the following must be an even intege

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