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

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Intern
Joined: 20 Feb 2012
Posts: 30
If x + y is an integer, is y an integer?  [#permalink]

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01 Mar 2012, 08:39
3
1
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:36) correct 50% (01:54) wrong based on 204 sessions

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 54434
Re: If x + y is an integer  [#permalink]

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01 Mar 2012, 08:46
5
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.

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Manager
Joined: 22 Feb 2012
Posts: 85
Schools: HBS '16
GMAT 1: 740 Q49 V42
GMAT 2: 670 Q42 V40
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WE: Corporate Finance (Aerospace and Defense)
Re: If x + y is an integer  [#permalink]

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01 Mar 2012, 08:44
1
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
Manager
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GMAT 1: 520 Q42 V19
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Re: If x + y is an integer, is y an integer?  [#permalink]

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01 Mar 2012, 08:58
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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Math Expert
Joined: 02 Sep 2009
Posts: 54434
Re: If x + y is an integer, is y an integer?  [#permalink]

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01 Mar 2012, 09:01
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]

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22 May 2014, 02:30
First statement

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

Hope this helps
Cheers!
J
Manager
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Re: If x + y is an integer, is y an integer?  [#permalink]

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22 May 2014, 03:35
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
Manager
Joined: 22 Sep 2012
Posts: 127
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If x + y is an integer, is y an integer?  [#permalink]

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22 May 2014, 08:18
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.
Intern
Joined: 20 May 2014
Posts: 3
Re: If x + y is an integer, is y an integer?  [#permalink]

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22 May 2014, 12:34
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
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Re: If x + y is an integer, is y an integer?  [#permalink]

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13 Jul 2017, 23:06
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Re: If x + y is an integer, is y an integer?   [#permalink] 13 Jul 2017, 23:06
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