Data Sufficiency Problem--GMAT Prep

[rehandossani]

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

[Ian Stewart]

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.

As you've written the question, the answer is certainly A, not D, for the reasons you mention. I've seen this question before, however, and I think a word is missing - if I remember correctly, the question tells you that p is odd. In that case, the answer is D.

edit - yes, I think the correction mentioned below is the one in the original question

[Skywalker]

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

[rehandossani]

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.