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

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.

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

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

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.

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

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.