Rows — In a row of 30 students facing North, what is R's position from the left end? Statements: I. There are 12 students between R and Q. II. T is 10th from the right end; there are 16 students between T and R.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: Statement II alone is sufficient; Statement I alone is not sufficient.
Explanation
Introduction / Context:Compute an absolute position using a fixed-size row and separations.
Given Data / Assumptions:
- Total = 30 students.
- I: Only distance between R and Q (no anchors).
- II: T is 10th from right; 16 between T and R.
Concept / Approach:Convert T's right-rank to a left-rank, then apply the 'k between' offset (k+1) and validate side feasibility.
Step-by-Step Solution:
From II: T's left-rank = 30 − 10 + 1 = 21.If R is to the right of T: R = 21 + 16 + 1 = 38 (invalid > 30). Hence R must be to the left: R = 21 − 16 − 1 = 4.Thus R is 4th from the left. Statement I alone has no absolute anchor and is insufficient.Verification / Alternative check:Bound checks ensure only the left-side placement is feasible, giving a unique result.
Why Other Options Are Wrong:
- A/C/D/E: II alone already yields a unique position.
Common Pitfalls:Forgetting to test both sides; forgetting the +1 offset.
Final Answer:B — Statement II alone suffices (R = 4th from left).