Direction: The following consists of a question and two statements numbered I…

Concept: In a Data Sufficiency question, a statement is sufficient only if it fixes the exact numeric value being asked for. A statement (or set of statements) that gives only the relative difference between unknown quantities — without anchoring even one of them to an actual known value — can never fix an exact value for any of them, however many such relative statements are combined.

Application: Let Rohit's rank = R (unknown).

1. From Statement I: Rohit's rank is 24 less than Nandani's rank, so Nandani's rank = R + 24. This only relates R to Nandani's rank, which is itself unknown — R stays undetermined. Statement I alone is not sufficient.

2. From Statement II: Archana's rank = R + 38, and Nandani's rank = Archana's rank − 10, so Nandani's rank = R + 28. Every value here is expressed only relative to R, with nothing anchored to an actual number. Statement II alone is not sufficient.

3. Combining Statement I and Statement II: together they still only describe how Rohit's, Nandani's, and Archana's ranks sit relative to one another — neither statement supplies a single absolute rank value or the total number of students that could pin R down to an actual number. So even together, Rohit's exact rank cannot be found.

Cross-check: Notice that Statement I gives Nandani's rank = R + 24, while Statement II gives Nandani's rank = R + 28 — two different expressions for the same quantity, so the exact numbers in the two statements are not fully consistent with each other. This does not change the conclusion, though: even a mutually consistent pair of purely relative-offset statements would still never anchor R to an actual number (no statement gives an absolute rank or the total class size), so the data remains insufficient either way — confirming that both statements together are not sufficient.

Hence, the correct choice is: statements I and II together are not sufficient.