Woozler wrote:109) 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.

Statement 1: When p is divided by 8 remainder is 5.
Thus p must be of the form (8n + 5), where n is a non-negative integer.
Thus, p = (8n + 5) = (8n + 4 + 1) = 4(2n + 1) + 1
Therefore when p is divided by 4, remainder is 1.

Sufficient.

Statement 2: p is the sum of the squares of two positive integers.
Thus p must be of the form 2(n² + m²), where n and m are positive integers.
If n and m both are even, p is divisible by 4 => remainder = 0
If n and m both are odd, p is not divisible by 4 => remainder may is 1 or 2 or 3

Not sufficient.

The correct answer is A.

My pleasure Woozler!