Gabrial is the 15th shortest student in his class. What is the total number of…

A Data Sufficiency question asks whether the given statements, alone or together, provide enough information to arrive at exactly one value for what is asked, not what that value happens to be. When people or items are ranked from one end (such as "nth shortest"), a rank explicitly described as the last one in that same direction equals the total count of people or items being ranked.

1. Gabrial's rank from the shortest end is given as 15.

2. Statement (i) alone: Hanak holds the last rank in that same shortest-to-tallest order. This says Hanak's rank equals the total number of students, but nothing links Hanak's position to Gabrial's, so the total stays unknown from this statement by itself.

3. Statement (ii) alone: Hanak's rank is exactly one away from Gabrial's rank of 15, so Hanak's rank is either 14 or 16. Without knowing whether Hanak is the last-ranked student, the total remains undetermined from this statement by itself.

4. Combining both: Hanak's rank equals the total (from Statement (i)) and also equals 14 or 16 (from Statement (ii)), so the total is either 14 or 16.

5. The question itself already fixes Gabrial's rank at 15, so the class must contain at least 15 students; a total of 14 is impossible.

6. That leaves exactly one valid total: 16.

Checking 16 against both statements: with 16 students ranked 1 (shortest) to 16 (tallest), Gabrial is 15th and Hanak, at rank 16, is both the last-ranked student and directly adjacent to Gabrial, consistent with Statements (i) and (ii) together. A total of 14 is ruled out purely because it would put Gabrial's own stated rank, 15, outside the class.

So neither statement pins down the total on its own, but together they fix it uniquely at 16: both statements together are sufficient.