In this task, you need to provide the correct option for a given problem from the provided options.

Input: Consider Input: Problem: if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12

Output: d

Input: Consider Input: Problem: how many even integers from 1 to 100 ( both inclusive ) have even number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7

Output: c

Input: Consider Input: Problem: if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Output: a