Final answer:
The true statement regarding searching algorithms is A, because the cost of sorting data is significant when data is infrequently searched, making binary search less efficient in such scenarios.
Step-by-step explanation:
When considering searching algorithms, the true statement is:
A. The cost of sorting data in order to use the binary search is of concern when the data is infrequently searched.
This is because the binary search algorithm requires the data to be sorted before it can be used effectively. Sorting data has its own computational cost, so if data is not searched frequently, the time spent sorting might not be justified.
Statement B is incorrect because binary search does not compare every element of an array; instead, it divides the array and eliminates half of the remaining elements in each step, significantly reducing the number of comparisons needed.
Statement C is incorrect as well, since sequential searching, or linear search, can locate a target in fewer comparisons than binary search if the target is near the beginning of the array. However, on average and especially with larger arrays, binary search is more efficient than sequential search if the data is pre-sorted.
Therefore, the correct answer to the student's question is option A.