Statement I: (2x + y) is an integer. 

• 2x + y is an integer. However, this does not necessarily mean that x and y are integers. 
• For example, x = 1.5 and y = 0.5 would satisfy this condition but (x + y) would not be an integer.

Statement II: (x + 2y) is an integer. 

• x + 2y is an integer. But this does not guarantee that x and y are integers. 
• For example, x = 0.5 and y = 1.5 would satisfy this condition but (x + y) would not be an integer.

Both the statements:

• However, if we combine both statements, we still can not tell that (x + y) would also be an integer. 
• Therefore, the question can be answered by using both statements together.

The correct answer is (d) 

• The Question cannot be answered even by using both the Statements together.