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


Option 1

x = 1.5 y = 2.5
so x+y = integer
x-y = integer

But taking x and y both integers too solve the above equation
Hence Insuff


Option 2

x+2y = integer

let x be any real no.. such that K is its decimal part
Y too be any real no. with L its decimal part
Since x+y= integer
so k+L = 10
LIKE
2.5+ 3.5
2.6+2.4
and list goes on......

But also given x+2y = Integer

k+ 2L = 10
this can only be possible when L = 0
which means

Suff

Hence IMO B

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

(1) x – y is an integer.
subtracting (1) from stem (x+y=integer) 2y=integer, y can be 1/2 or any integer. not sufficient

(2) x + 2y is an integer
subtracting stem (x+y=integer) from (2) we get y=integer, hence B

Nice work guys!