$32^5 + 2^{27}$ is divisible by

Let $p$ and $q$ be positive integers satisfying $p < q$ and $p + q = k$. What is the smallest value of $k$ that does not determine $p$ and $q$ uniquely?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

If the average marks in a class are 60, then what is the number of students in the class?

Statement-I:

The highest marks in the class are 70 and the lowest marks are 50.

Statement-II:

Exclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

Is $(x + y)$ an integer?

Statement-I:

$ (2x + y) $ is an integer.

Statement-II:

$ (x + 2y) $ is an integer.

Which one of the following is correct in respect of the above Question and the Statements?