If p and q are two different odd prime numbers, such that p < q, then which of the following must be true?
Choose the correct choice from the following answers:	A) (2p + q) is a prime number	B) p + q is divisible by 4	C) q - p is divisible by 4	D) (p + q + 1) is the difference between two perfect squares of integers	E) p2+q2 is the difference between two perfect squares of integers
1. (2p + q) for sure is an odd number , but may or may not be a prime number .   Eg - if we take 3 and 5 as p and q resp, we get 11, which is a prime number.   But if we take 7 and 11, we get 25, which is not a prime number.   2. p + q for sure gives us an even number. It may or may not be divisible by 4.   Eg - (7 + 5) = 12 , which is divisible by 4. But   (11 + 7)= 
<gadget id="calculator">  (11 + 7)</gadget>
<output>18</output>
18 , not divisible by 4   3. Same way as 2nd.   4. (p + q + 1) gives us an odd number.   Lets see the trend of difference between squares of consecutive integers.   2^2 - 1^2= 3   3^2 - 2^2 = 5   4^2 - 3^2 = 7   5^2 - 4^2 = 9   6^2 - 5^2 = 11 and so on.   The trend is : The difference between squares of consc. integers is always odd number. And it covers all the odd numbers.   However , when we don't take consecutive integers, this trend is not followed.   Eg : 5^2 - 3^2 = 16 , which is an even number   3^2 - 1^2 = 8 , again not an odd number   Hence : Any odd number can be expressed as the difference of the squares of integers.   5. (p^2 + q^2) gives an even number.   ANSWER:(p + q + 1) is the difference between two perfect squares of integers
<result>D</result>
If p and q are two different odd prime numbers, such that p < q, then which of the following must be true?