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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
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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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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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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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2
$$x=y+2$$ ---->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

##### General Discussion
Math Expert
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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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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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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: 7765
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
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Re: If x = y + 2 and x is an even integer, which of the following could be  [#permalink]

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22 Oct 2018, 13:29
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

Given that x is even then y must be even.

x + y = y + 2 + y = 2y +2

2 (y+1) = even number

try $$\frac{140}{2} = 70 - 1 = 69$$ not even not possible.

Try $$\frac{146}{2} = 73 - 1 = 72$$ even and makes x = 74 possible.

$$\frac{148}{2} = 74 - 1 = 73$$ not possible

$$\frac{152}{2} =76 - 1 = 75$$ not possible.

$$\frac{156}{2} = 78 - 1 = 77$$ not possible.

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

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23 Oct 2018, 19:22
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

We see that x + y must be the sum of 2 consecutive even integers, or y + (y + 2) = 2y + 2. We also see that both x and y are even integers.

If we subtract 2 from each answer choice we have:

138, 144, 146, 150, and 154

When we divide those answers by 2, the only one that provides an even quotient is 144, since 144/2 = 72.

Alternate Solution:

We know that x = y + 2, and x is even, so we know that y is also even. By substitution, we see that x + y = (y + 2) + y = 2y + 2.

Let’s check each answer choice. We are looking for an answer choice that yields an even integer value for y:

Choice A: Does 2y + 2 = 140 yield an even integer value for y? No. In this case, y = 69.

Choice B: Does 2y + 2 = 146 yield an even integer value for y? Yes! In this case, y = 72.

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

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12 Nov 2018, 06:28
x is even, so x=2k
x=y + 2 --> y=2k - 2
this means:
x + y = 2k + 2k -2 = 4k -2

only 146 satisfies 4k - 2.
Re: If x = y + 2 and x is an even integer, which of the following could be   [#permalink] 12 Nov 2018, 06:28
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