Are there any prime numbers between the integers m and n?

Statement 1: for m-n to be even, either both should be odd or even. There can or cannot be a prime number between two even or two odd integers. For instance, Between 4 and 6, 5 is a prime number, but there is no prime number between 45 or 47.
This statement is not sufficient to solve the problem


Statement 2: There is only one odd number between m and n.

In this case, m and n can be even/odd but only one odd number should be between them
Case 1: 5, 6, 7, 8, 9
possible values of m and n are : m=5, n=8
m=6, n=8
m=5, n=9
m=6, n=9

For any of the above values of m and n , there is a prime number, 7 between m and n

Case 2: 7, 8, 9 , 10, 11
possible values of m and n are : m=7, n=10
m=7, n=11
m=8, n=10
m=8, n=11
For any of the above values of m and n , there is no prime number between m and n

This statement is not sufficient to solve the problem


Combining both statements:

Both m and n are either odd or even and there is only one odd between m and n
Case 1: 5, 6, 7, 8, 9

possible values of m and n are :
m=6, n=8
m=5, n=9

For any of the above values of m and n , there is a prime number, 7 between m and n

Case 2: 7, 8, 9 , 10, 11
possible values of m and n are :
m=7, n=11
m=8, n=10
For any of the above values of m and n , there is no prime number between m and n

Combining both statements does not resolve the problem, so the correct answer is E.

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