Raghu got the 20th rank among all the students in the class. How many students…

Concept: In a rank-based data-sufficiency problem, a student's rank counted from the top (R_top) and rank counted from the bottom (R_bottom) in a class of N students are linked by the identity N = R_top + R_bottom - 1. The class size N is uniquely determined ONLY IF every rank-pair (R_top, R_bottom) admitted by the given statements yields the SAME value of R_top + R_bottom - 1; if different admissible pairs give different sums, N is left undetermined even though each individual statement may look informative.

Application:

1. Statement 1 alone: "second-last" fixes only Rajive's rank from the bottom, R_bottom(Rajive) = 2. It gives no rank from the top and no link to Raghu at all, so N cannot be computed from it alone.

2. Statement 2 alone: "next to Raghu" only relates Rajive's rank from the top to Raghu's rank (20), giving two candidates: R_top(Rajive) = 19 or R_top(Rajive) = 21. It says nothing about Rajive's distance from the bottom, so N still cannot be computed from it alone.

3. Both together: using N = R_top + R_bottom - 1 with R_bottom(Rajive) = 2, N = R_top(Rajive) + 1. Statement 2 supplies two possible values for R_top(Rajive) (19 or 21), so substituting each gives two candidate class sizes: N = 20 and N = 22, not one.

Cross-check: test both candidates against every condition in the problem.

Both N = 20 and N = 22 satisfy every stated condition without contradiction. Since two different class sizes remain equally valid even after combining both statements, the class size is not uniquely determined.

Result: Even both statements put together are not sufficient to solve the problem.