In this scenario, Substitution is the best way of solving.
Let the value of Q be 3, then the set = (119,120,121) and the largest integer in the set = 121. Now, let us substitute the value of Q(=3) in the options.
A)(Q-1)/2 + 120 = 121 - perfect, and is the answer
B)Q/2 + 119 = 120.5
C)Q/2 + 120 = 121.5
D)(Q+119)/2 = 61
E)(Q+120)/2 = 61.5
Another approach:
You can easily eliminate three options on first look. Since Q is an odd integer.
A)(Q-1)/2 + 120 = (Odd-1)/2 + 120 = (Even/2)+120 = Integer - can be the answer
B)Q/2 + 119 - odd/2 + 119 = Not an Integer - cannot be the answer
C)Q/2 + 120 - odd/2 + 120 = Not an Integer - cannot be the answer
D)(Q+119)/2 - (odd+119)/2 = Integer - can be the answer
E)(Q+120)/2 - (odd+120)/2 = Not an Integer - cannot be the answer.
We, now, have two options to choose from. Let us substitute the value of Q = 3, the largest(and only) number is 121.
A)(Q-1)/2 + 120 = (3-1)/2 + 120 = 121
D) (Q+119)/2 = (3+119)/2 = 61. So option A is correct.
