If the bank has 100 lockers each needing a numeric code, which option covers the maximum range for the codes available?

In the context of code generation for the bank's 100 lockers, the main goal is to maximize the range of available numeric codes. Each locker can be assigned a unique code, and the correct answer encompasses the widest range of potential codes.

Choosing all evens would mean assigning codes only to even numbers. Even numbers follow the pattern of 0, 2, 4, 6, etc. While this set does provide a considerable range, the range is still limited in comparison to the option that combines both odds and evens.

A better choice is the combination of odds and evens, which includes every integer. This option allows codes to be assigned from the entire set of natural numbers, thereby offering a much broader range. By including both odd and even numbers, you effectively double the available choices compared to merely selecting from evens or odds alone.

This means all lockers can be assigned distinct codes from a continuum of numbers, promoting maximum utilization of space and uniqueness for each locker combination. In other words, the combination of odd and even codes ensures that you have the full spectrum of codes available, rather than being restricted to only one category.