Number properties ! this is killing me !!

x+y is integer

A
x – y is an integer

so add both
2x integer
but no info about x

so no infor about y


other sub
x+y
x-y subtract
2y integer
but no info for y




B
x + 2y is an integer
and
x + y is an integer

so y has to be integer

ans IMO is B
whats the OA?

Hi Vishu,
The approach to thsi DS question would be as i believe


here the given data is

x + y = int

here in y may or may not be int

for eg

3 + 3 = 6-- here y is int(3)
5.2 + 0.8 = 6 --here y is not int(0.8)

now consider the statement 1

x - y = int

here again y may or may not be int henec i guess thsi sis insufficient

consider statement 2

x + 2y = int

for eg x = 2 and y = 3
the x + 2y = 8 (here y is 6 int)

now suppose x = 3 and y = 0.2

then x + 2y = 3.4(this cannot be true as the answer has to be int,henec the value of y in this case can never be non int,it has to be always int

hence teh statement 2 seem sto be sufficient

So the answer would be B
Whatz the OA? is there any other approach anyone can put light on ?

Thanks

It is B indeed jsut wandering why i went wrong !

thanbks u guys

Vishu

An easier way to solve this one without any substitution:

Given: X+Y=int_0
Prove: Y=int?

1) X-Y=int_1

Subtract prompt equation from eq in 1:
X-Y=int_1
-(X+Y)=int_0
-2Y=int_1+int_0

This tells you that Y is the sum of two integers. Because we don't know if int_1 and int_0 are even or odd we cannot say if (int_1+int_0)/2 is a integer.

INSUFFICIENT

2) X+2Y = int_2

Notice you can write this as:
X+Y+Y = int_2
[subbing in the given equation]
int_1+Y=int_2
Y=int_1-int2 -> Y is the sum of two integers and is therefore sufficient.

SUFFICIENT

Answer is B.