Concept: The question tests on basics in statistics
For such questions, assuming values/plugging in is the best approach that can give accurate and quick results.
For example, consider a simple value of 3 for Q
Then we are given that the median of 3 consecutive integers is 120
=> The 3 numbers would be 119,120 and 121
=>The largest integer is 121
=>Plug in the values of Q=3 to see which option yields 121
In option A which is (Q-1)/2 + 120 we have 1 + 120 =121