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

Question

(1) x – y is an integer.
(2) x + 2y is an integer.

Bunuel · Accepted Answer

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.

AbeinOhio · Answer

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

GMATD11 · Answer

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

Bunuel · Answer

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

Answer to the question is B, not E.

jlgdr · Answer

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
Cheers!
J

DesiGmat · Answer

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

kinghyts · Answer

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.

ChiragBhagat · Answer

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

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

It is known that x + y is an integer.
We have to find out if y is an integer.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  x – y is an integer.
From the question, x + y is an integer.

x + y = integer

x – y = integer

Adding the two equations, we have, 2x = integer. x could be an integer or a fraction and still satisfy this equation. 
However, we do not have any data about y.

The data in statement 1 is insufficient to find out if y is an integer.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  x + 2y is an integer.
From the question, x + y is an integer.

x + y = integer

x + 2y = integer

Subtracting equation 1 from equation 2, y = integer

The data in statement 2 is sufficient to say that y is an integer.
Statement 2 alone is sufficient. Answer option C and E can be eliminated.

The correct answer option is B.

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

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