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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: 47168
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
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25% (medium)

Question Stats:

76% (01:12) correct 24% (01:32) wrong based on 123 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

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Joined: 13 Oct 2016
Posts: 367
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
3
$$x=y+2$$ ---->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

Math Expert
Joined: 02 Aug 2009
Posts: 6274
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
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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 12 Aug 2015
Posts: 2648
GRE 1: Q169 V154
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
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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Joined: 20 Mar 2017
Posts: 1
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 ?
Math Expert
Joined: 02 Aug 2009
Posts: 6274
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

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