In a school, there are a total of 88 students in three sections, A, B, and C.…

A pair of data-sufficiency statements is sufficient only when applying it, together with every stated constraint, pins down exactly one valid value for what is asked. Here, the constraints are: the three sections' student counts are distinct positive integers that add up to 88, and section B holds the largest count of the three.

1. Statement I alone: it says one section has two students fewer than B (that section = B minus 2). This only fixes a relationship between two sections; it gives no actual count, so B cannot be found from this alone.

2. Statement II alone: it says one section has 23 students. Since B is the largest of three distinct positive integers summing to 88, B itself cannot be 23 - if B were 23, the other two sections would each have to be smaller and distinct, so at most 22 and 21, giving a total of at most 66, short of 88. So the 23-student section must be one of the non-B sections, but this alone still leaves many different valid values for B (many different distinct pairs for the other non-B section and B can sum with 23 to 88), so B cannot be pinned down from this statement alone.

3. Combining both statements: the '23-student' section and the 'B minus 2' section can relate to the three sections A, B, C in only three possible ways.

4. Case (i) - the same section is both 'B minus 2' and '23': then B minus 2 = 23, so B = 25, and the third section = 88 minus 25 minus 23 = 40. But 40 is greater than 25, so that section would exceed B, contradicting that B is the maximum. Invalid.

5. Case (ii) - 'B minus 2' and '23' are two different sections, with B as the third: then B + (B minus 2) + 23 = 88, giving 2B = 67, so B = 33.5, not a whole number of students. Invalid.

6. Case (iii) - B itself is the section with 23 students: then the other section is B minus 2 = 21, and the third section = 88 minus 23 minus 21 = 44. But 44 is greater than 23, so that section would exceed B again, contradicting that B is the maximum. Invalid.

7. Every possible way of applying both clues together either produces a fractional student count or breaks the rule that B is the largest section. So no consistent value of B exists even when both statements are combined.

Checking directly: is there any set of three distinct positive integers summing to 88, with the largest one equal to B, one other section equal to B minus 2, and one section equal to 23? The three cases above are exhaustive, since the '23' section must be the 'B minus 2' section, a different section, or B itself, and each case fails, confirming there is no valid assignment.

Since neither statement alone, nor both together, fix a valid value for B, the correct choice is: even both statements together are not sufficient to answer the question.