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

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Bunuel
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If x and y are integers, which of the following must be an even intege [#permalink] New post   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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D
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Bunuel
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Re: If x and y are integers, which of the following must be an even intege [#permalink] New post   12 Mar 2018, 21:50
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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


2. Properties of Integers



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Re: If x and y are integers, which of the following must be an even intege [#permalink] New post   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
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Re: If x and y are integers, which of the following must be an even intege [#permalink] New post   13 Mar 2018, 11:57
Ans D

X and y are integers

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

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If x and y are integers, which of the following must be an even intege [#permalink] New post   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] New post   15 Mar 2018, 10:14
Expert Reply
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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Jansaida
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Re: If x and y are integers, which of the following must be an even intege [#permalink] New post   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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