The ques says to find no. of comp inorder to find a number(Say 'K') in sorted array more than n/2 times.
Now Just saying that check with the middle element won't work as Eg:-
1,1,2,3,3 Here middle element is 2 but kits not more than n/2 times , therefore O(1) is not possible acc. to me,
Now with Binary Search Once You can find the first index of that Number K in logn time, and in another logn time of binary search to find the last index, now checkthe difference of the two positions to be more than n/2 , Hence overall O(logn) comparisons needed.