Which is correct regarding the statement: “if x is an odd integer, then the median of x , x + 2, x + 6, and x + 10 is an odd number” a.) the statement is sometimes true b.) the statement is always false c.) the statement is always true d.) there is not enough information provided to answer the question

X is an odd number 

x+2 is also odd (consider the example x = 3 so x+2 = 3+2 = 5). Adding 2 to any odd number is always odd

Similarly, so is x+6 (since we have x+2+2+2).  

And so is x+10 (x+2+2+2+2+2). 

So every value in this list is an odd number. The middle most values are x+2 and x+6 which are both odd.

Adding any two odd numbers together yields an even number. For example 3+5 = 8. Divide this even number in half and we may or may not get an odd number (eg: 8/2 = 4 and 6/2 = 3)

So this statement is sometimes true