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# If x = y + 2 and x is an even integer, which of the following could be

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Math Expert
Joined: 02 Sep 2009
Posts: 42281

Kudos [?]: 132984 [0], given: 12400

If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Dec 2016, 06:13
Expert's post
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Question Stats:

77% (01:16) correct 23% (01:39) wrong based on 110 sessions

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If x = y + 2 and x is an even integer, which of the following could be the sum of x and y?

A. 140
B. 146
C. 148
D. 152
E. 156
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132984 [0], given: 12400

Senior Manager
Joined: 13 Oct 2016
Posts: 367

Kudos [?]: 402 [1], given: 40

GPA: 3.98
Re: If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Dec 2016, 06:34
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$$x=y+2$$ ---->if $$x$$-even then $$y$$ must be even too

$$x+y = y+y+2 = 2y+2 = 2(y+1) = 2(even+1) = 2*odd$$

$$\frac{x+y}{2} = odd$$

A) 140/2 = 70 even
B) 146/2 = 73 odd
C) 148/2= 74 even
D) 152/2 = 76 even
E) 156/2 = 78 even

Kudos [?]: 402 [1], given: 40

Math Expert
Joined: 02 Aug 2009
Posts: 5223

Kudos [?]: 5868 [1], given: 118

Re: If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Dec 2016, 06:44
1
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Expert's post
Bunuel wrote:
If x = y + 2 and x is an even integer, which of the following could be the sum of x and y?

A. 140
B. 146
C. 148
D. 152
E. 156

Another way to look at it..
Both x and y are even but ONLY one will be divisible by 4 and other will be not, so their SUM will not be divisible by 4..
ONLY B is not div by 4
B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5868 [1], given: 118

Retired Moderator
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 876 [1], given: 602

Re: If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Dec 2016, 09:31
1
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Fabulous..!! chetan2u
+1 to you.

Here is what i did-->
I took the long route.
x-> Even
So y->Even

Option 1->
x+y=140
2y+2= 140
2y=138
y=> odd => Rejected

Option 2->
x+y=146
2y=144
y=72
Hence x=74
Acceptable.
Hence B

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Kudos [?]: 876 [1], given: 602

Intern
Joined: 20 Mar 2017
Posts: 1

Kudos [?]: 0 [0], given: 11

If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Sep 2017, 01:19
chetan2u wrote:
Bunuel wrote:
If x = y + 2 and x is an even integer, which of the following could be the sum of x and y?

A. 140
B. 146
C. 148
D. 152
E. 156

Another way to look at it..
Both x and y are even but ONLY one will be divisible by 4 and other will be not, so their SUM will not be divisible by 4..
ONLY B is not div by 4
B

Hi chetan2u
I dont understand why only 1 will be divisible by 4 and other will not be. Can you please explain ?

Kudos [?]: 0 [0], given: 11

Math Expert
Joined: 02 Aug 2009
Posts: 5223

Kudos [?]: 5868 [0], given: 118

Re: If x = y + 2 and x is an even integer, which of the following could be [#permalink]

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10 Sep 2017, 02:41
Thiyag wrote:
chetan2u wrote:
Bunuel wrote:
If x = y + 2 and x is an even integer, which of the following could be the sum of x and y?

A. 140
B. 146
C. 148
D. 152
E. 156

Another way to look at it..
Both x and y are even but ONLY one will be divisible by 4 and other will be not, so their SUM will not be divisible by 4..
ONLY B is not div by 4
B

Hi chetan2u
I dont understand why only 1 will be divisible by 4 and other will not be. Can you please explain ?

Hi..

You pick up any two consecutive even integer, one will be multiple of 4 & other not..
Say you pick y=2, x=2+2=4..... Only x is div by 4
Pick y as 4, x=4+2=6..... Only y is MULTIPLE of 4
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5868 [0], given: 118

Re: If x = y + 2 and x is an even integer, which of the following could be   [#permalink] 10 Sep 2017, 02:41
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