Data Sufficiency (DS) | If p, x, and y are positive integers, y is odd, and p = x^2

I did this question this way. I found it simple.

1. p=x^2+y^2
y is odd
p div 8 gives remainder 5. A number which gives remainder 5 when divided by 8 is odd.

so (x^2 + y^2)/8 = oddnumber
(x^2 + y^2) = 8 * oddnumber (this is an even number without doubt)

x^2 + y^2 is even. Since y is odd to get x^2+y^2 even x must also be odd.

X is an odd number not divisible by 4

Option A: 1 alone is sufficient