Data Sufficiency

If p is positive integer, what is remainder when p is divided by 4?
a. When P is divided by 8 remainder is 5
b. P is the sum of the squares of two positive integers.

My answer was A

Reasoning:

a) p = 8x + 5. When divided by 4, it will always give a remainder 1. So Suff

for (b) if 3^2 + 1^2 = 10, when divided by 4, gives remainder 2. However when 2^2 + 1^1 = 5, divided by 4 gives a remainder 1. So insuff.

However this answer is wrong. Can someone please explain why the answer should be D

Hi,

Is the option b "b. P is the sum of the squares of two positive integers. " OR
"b. P is the sum of the squares of two consecutive positive integers. " ?

Thanks

Well actually, I saw this question in 198 700+ GMAT Prep question. Only "square of positive integers" is written. But yeahif its has been consecutive positive integers than the answer would D.