Data Sufficiency – Ranks from top and bottom (class strength inference) Question: Gaurav ranks 18th from the top in his class. What is his rank from the last? Statements: I. There are 47 students in the class. II. Jatin, who ranks 10th from the top in the same class, ranks 38th from the last.
Correct Answer: Either I or II is sufficient
Introduction / Context:This DS item tests rank conversion using total class size. If you know the class strength N and a student's rank from the top r, the rank from the bottom is N − r + 1. We assess whether each statement alone gives N.
Given Data / Assumptions:
- Known from the question: Gaurav is 18th from the top.
- I: Class size N = 47.
- II: Jatin is 10th from the top and 38th from the bottom.
Concept / Approach:The conversion formula is rank_from_bottom = N − rank_from_top + 1. So we only need to know N. Either a direct statement of N or an inference that yields N is sufficient.
Step-by-Step Solution:
Using I alone: N = 47. Then Gaurav's rank from the bottom = 47 − 18 + 1 = 30. Hence I alone is sufficient.Using II alone: For any student, rank_top + rank_bottom − 1 = N. So N = 10 + 38 − 1 = 47. With N known, Gaurav's rank from the bottom is again 47 − 18 + 1 = 30. Hence II alone is also sufficient.Verification / Alternative check:Both methods yield the same class size (47) and hence the same answer (30 from the last), confirming each statement's sufficiency independently.
Why Other Options Are Wrong:
- I alone or II alone only: both are sufficient, not just one.
- Neither: false because each alone suffices.
- Both: stronger than necessary in DS.
Common Pitfalls:Omitting the +1 in the conversion formula; mixing up top vs bottom ranks; assuming tie ranks (not stated).
Final Answer:Either I or II is sufficient