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If x + y is an integer, is y an integer?

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If x + y is an integer, is y an integer? [#permalink] New post 01 Mar 2012, 07:39
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If x + y is an integer, is y an integer?

(1) x – y is an integer.
(2) x + 2y is an integer.
[Reveal] Spoiler: OA
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Re: If x + y is an integer [#permalink] New post 01 Mar 2012, 07:44
I would say B..

Here is my solution:
1)
X + Y = int could mean 4.5+3.5= int and
X-Y = 4.5-3.5=int
so there is an exception for A - then i eliminate D

2) X-2Y=INT (this and X+y = int) only if all items are integers
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Re: If x + y is an integer [#permalink] New post 01 Mar 2012, 07:46
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If x + y is an integer, is y an integer?

(1) x – y is an integer --> if x=y=0.5 then the answer to the question is NO but if x=y=1 then the answer to the question is YES. Not sufficient.

(2) x + 2y is an integer --> x+2y=(x+y)+y=integer. Since given that x+y=integer, then: integer+y=integer --> y=integer. Sufficient.

Answer: B.
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Re: If x + y is an integer, is y an integer? [#permalink] New post 01 Mar 2012, 07:58
if x+y = integer Is y integer?
1.5+0.5 = integer
2+1 = integer

a) x-y=integer
2-1 = integer
1.5-.5 = integer ---NS

b) x+2y = integer

1+2(0.5) = integer
1+2(3) = integer ---NS
a+b)
NS

E
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Re: If x + y is an integer, is y an integer? [#permalink] New post 01 Mar 2012, 08:01
Expert's post
GMATD11 wrote:
if x+y = integer Is y integer?
1.5+0.5 = integer
2+1 = integer

a) x-y=integer
2-1 = integer
1.5-.5 = integer ---NS

b) x+2y = integer

1+2(0.5) = integer
1+2(3) = integer ---NS
a+b)
NS

E


x=1 and y=0.5 violates given statement that x+y=integer.

Answer to the question is B, not E.
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Re: If x + y is an integer, is y an integer? [#permalink] New post 10 Oct 2013, 04:42
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Re: If x + y is an integer, is y an integer? [#permalink] New post 22 May 2014, 01:30
First statement

Add x+y = Integer
x - y = Integer

2x is Integer + Integer

Now if Integer + Integer is in fact even then x is an intege
But if Integer + Integer = Odd then X is NOT an integer

Therefore insufficient

Second statement

x+2y = Integer
x + y + y is an integer

We already know that x+y is an integer, therefore 'y' left must also be an integer

Sufficient

Answer: B

Hope this helps
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Re: If x + y is an integer, is y an integer? [#permalink] New post 22 May 2014, 02:35
Option B is correct.

Statement 2) x+2y is an integer -> (x+y) + y - > (x+y) is an integer (given)
now integer + y = integer
hence Y is an integer because (integer - integer) results in an integer
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Re: If x + y is an integer, is y an integer? [#permalink] New post 22 May 2014, 07:18
Here is my approach :-

1) x+y = Integer
x-y = Integer

if we consider x = 2 and y=0.5, then the 2 equations are met and y is not an integer
if we consider x = 2 and y=1, then also the 2 equations are meant and this time y is an integer
Clearly, insufficient

2.) x+2y = Integer
x+y = Integer

If we subtract the second from the first, we get y as Integer since integer subtracted from an integer would an integer
Sufficient.
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Re: If x + y is an integer, is y an integer? [#permalink] New post 22 May 2014, 11:34
Difference or Sum of two integers is always an integer.

We can use x+y & x-y to arrive at 2y & 2x being integers.

We can use x+y & x+2y to arrive at y & 2x+3y being integers.

Hence statement 2 is sufficient to arrive at y being integer.

Thanks,
Chirag Bhagat
Re: If x + y is an integer, is y an integer?   [#permalink] 22 May 2014, 11:34
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