hi i`ll try to handle with 2 st 1 is clearly insufficient
(2) (x+y)=8k where k is an integer
x=8k-y
x^2-y^2=(8k-y)^2-y^2=64k^2-16ky+y^2-y^2=64k^2-16ky=16(4k^2-ky) -divisible by 8
my pick for B

anjaneiya wrote:Is (x^2-y^2) divisible by 8?

1) x and y are even integers.
2) (x+y) is divisible by 8.

[spoiler] B/C....?[/spoiler]

source- gmatclub.

(x^2-y^2) = (x+y) * (x-y)

1. x and y both even.

say x = 4, y = 2 then (x^2-y^2) = (x+y) * (x-y) = 12 not divisible by 8.
say x = 2, y = 0 then (x^2-y^2) = (x+y) * (x-y) = 4 not divisible by 8.
say x = 2, y = 2 then (x^2-y^2) = (x+y) * (x-y) = 0 divisible by 8.

Insufficient.

2. (x+y) is divisible by 8

Multiple anything with 8 is a multiple of 8. However, when x and y are not integers then it will not suffice.

Take this x = 5.2 and y = 3.8 then though x+y is div by 8, x-y is not.

Thus, insufficient.

Combine both, we will get definite integers for x and y. And any integer multiplication to a multiple of 8 is always div by 8.

IMO C

My answer to this question = B. As a few people noted, Statement 1 is insufficient by itself since (6,2) yields a positive response while (6,4) yields a negative response.

Another way of writing X^2 - Y^2 = (X+Y)(X-Y)

Statement 2 says that (X+Y) is divisible by 8. So, (X+Y) is some multiple of 8. Regardless of the value of (X-Y), one of the factors of this product is 8. For instance, if (X+Y) = 16, the two factors of this product are 8 and 2*(X-Y).
Thus, X^2 - Y^2 is divisible by 8, and Statement 2 is sufficient on its own.

anjaneiya wrote:Is (x^2-y^2) divisible by 8?

1) x and y are even integers.
2) (x+y) is divisible by 8.

[spoiler] B/C....?[/spoiler]

source- gmatclub.

x^2-y^2= (x+y)*(x-y)

Statement (1) (x+y)*(x-y)/8 - ? either (x+y)*(x-y) or (x+y) and (x-y) must be divisible by 8. One possibility is to test with the consecutive even integers; this returns false about Statement (1) -Not sufficient

Statement (2) (x+y)*(x-y)/8 - ? (x+y)/8=i (integer) and 8i*(x-y)/8= i*(x - y) therefore regardless of x and y values we have a true statement - Yes the expression can be divided by 8. Statement (2) -Sufficient.

Answer B.

As shovan85 above points out, we don't know whether x and y are integers. x can be 5.2 while y is 2.8. Then, x + y is 8 but x - y is a non-integer.

If we muliply a non-integer by 8, is the result a multiple of 8?