Data Sufficiency – Determine P’s rank from the bottom (n = 30) Question: In a class of 30 students, what is the rank of P from the bottom? Statements: I. M is third from the top and there are five students between M and P. II. K is fourth from the bottom and there are 17 students between K and P.

Introduction / Context:This DS question asks for P’s bottom rank in a class of 30. Each statement provides relative positioning that may allow a unique absolute rank for P. We check each independently.

Given Data / Assumptions:

• Total students N = 30 (given in the question text).
• I: M is 3rd from the top; there are exactly five students between M and P.
• II: K is 4th from the bottom; there are exactly 17 students between K and P.
• No ties; positions are integers 1..30 from the top.

Concept / Approach:If there are x students between two ranks r1 and r2, then |r1 − r2| = x + 1. Use this to derive P's top rank and convert to bottom rank by N − r_top + 1.

Step-by-Step Solution:

Verification / Alternative check:Both statements independently yield the same unique rank for P (9th from the top, 22nd from the bottom), confirming each suffices.

Why Other Options Are Wrong:

• I alone only / II alone only: both are sufficient, not just one.
• Neither: false because each alone works.
• Both: true but not the minimally sufficient DS choice.

Common Pitfalls:Misinterpreting 'between' (remember to add 1 when converting to rank difference); forgetting to convert bottom to top ranks correctly.

Final Answer:Either I or II is sufficient