Why is Binary Search a divide and conquer algorithm?

Question

I was asked if a Binary Search is a divide and conquer algorithm at an exam. My answer was yes, because you divided the problem into smaller subproblems, until you reached y

Answer 1

A proper divide and conquer algorithm will require both parts to be processed.

Therefore, many people will not call binary-search a divide and conquer algorithm, it does divide the problem, but discards the other half.

But most likely, your examiners just wanted to see how you argue. (Good) exams aren't about the facts, but about how you react when the challenge goes beyond the original material.

So IMHO the proper answer would have been:

Well, technically, it consists only of a divide step, but needs to conquer only half of the original task then, the other half is trivially done already.

BTW: there is a nice variation of QuickSort, called QuickSelect, which actually exploits this difference to obtain an on average O(n) median search algorithm. It's like QuickSort - but descends only into the half it is interested in.