Question

If q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers

Answer 1

Let Q=3, implying that there are 3 consecutive integers. 
Since the median is 120, the 3 integers are {119, 120, 121}. 
The question stem asks for the largest integer: 121. 
This is our target. 
Now plug Q=3 into the answers to see which yields our target of 121. 
Only   (Q-1)/2 + 120 :
(Q-1)/2 + 120 = (3-1)/2 + 120 = 121. 

The correct answer is 
 (Q-1)/2 + 120