Data Sufficiency

What is the sum of positive integers x & y?

1. x^2+2xy+y^2=16

2. x^2-y^2=8

IMo A

the sum of positive integers x & y?

1. x^2+2xy+y^2=16
Sufficient
=>( X+y)^2 = 16
=> X+y= 4

X+y= -4 is not possible because X and Y are positive

2. x^2-y^2=8

( x+Y) ( X- Y) = 8

Insufficient

So A

I think the answer is D

A is sufficient as explained earlier.

Here is how B is sufficient:

(x+y)(x-y)=8

Since x and y are positive integers, only combinations of (x+y)(x-y) possible are (8*1) and (4*2). We will see that(x+y)(x-y)= (8*1) gives x and y in decimal. So the only solution is

(x+y)(x-y)=4*2 => (x+y)= 4 or (x+y)= 2.

But (x+y) = 2 gives negative y so the only solution for (x+y) is 4

Mustang wrote:I think the answer is D

But (x+y) = 2 gives negative y

Can you please elaborate more on this?
As I see it, both x and y can =1

Mustang

Thanks! Agreed D

8 can be expressed in terms of Positive numbers as 1* 8 or 4*2

1*8 X+y = 8 and X-Y = 1 Solvng this yields non integer values for X and Y

4*2
Yields x = 3 and Y = 1 so sum = 4

A is not suf, because it can 1 & 3 or 2 & 2.

A and B together is Suf, because 2^2 - 2^2 = 0 while 3^2 - 1^2 = 8

Now I think B alone is suf as I cannot find any other two pos ints other than 3 and 1 that X^2-Y^2 = 8. But I am not sure.

I would guess B on this one, but it could be C, I am not sure.

lilu wrote:

Mustang wrote:I think the answer is D

But (x+y) = 2 gives negative y

Can you please elaborate more on this?
As I see it, both x and y can =1

I apologize for not explaining clearly:

when I said (x+y)=2, I meant (x+y)=2 and (x-y)=4 both should be satisfied. if you solve both of this together , y will be negative. Hope this clarifies

Reader wrote:A is not suf, because it can 1 & 3 or 2 & 2.

A and B together is Suf, because 2^2 - 2^2 = 0 while 3^2 - 1^2 = 8

Now I think B alone is suf as I cannot find any other two pos ints other than 3 and 1 that X^2-Y^2 = 8. But I am not sure.

I would guess B on this one, but it could be C, I am not sure.

Reader: Note that we are only interested in finding x+y (irrespective of the individual values). x+y will always be = 4 so A is sufficient

Mustang wrote:

Reader wrote:A is not suf, because it can 1 & 3 or 2 & 2.

A and B together is Suf, because 2^2 - 2^2 = 0 while 3^2 - 1^2 = 8

Now I think B alone is suf as I cannot find any other two pos ints other than 3 and 1 that X^2-Y^2 = 8. But I am not sure.

I would guess B on this one, but it could be C, I am not sure.

Reader: Note that we are only interested in finding x+y (irrespective of the individual values). x+y will always be = 4 so A is sufficient

I somehow missed "sum"...