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.

Difficulty: Medium

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).

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