Hi Needgmat,
Below three points will be helpful for you, if you are solving questions about the perfect square.
 1. A perfect square will always have an odd number of factors
 2. A square of a prime number will always have exactly 3 factors
 3. A perfect square will have an odd number of odd factors and even number of even factors
From the first line of the question, it's clear that it is a perfect square.
Also Basic rule for a perfect square is that,
If N is a perfect square and expressed as p^x * q^y * r^z ....(where p, q and r are prime numbers) Then x , y and z are divisible by 2.
Also this is a must be question.
Remember to Plug in.
I. P² has an odd number of positive factors
- this goes by the rule no.1(A perfect square will always have an odd number of factors) or just plug in 36 is a perfect square where the number of factors are odd = 9. So true. So eliminate answer choices B, C and E.
II. P² can be expressed as the product of an even number of positive prime factors .
This goes by the definition of the perfect square. So true. Eliminate the answer choice A. Answer has to be D. no need to check the third statement. Plug in No need here.
III. P² has an even number of positive factors - this is against the first rule((A perfect square will always have an odd number of factors)) mentioned above. So this is not true.
So the answer is D.
Hope this helps.
Would like to know the source of this question? Its poorly framed because statement I and III are just opposite to each other.
