Seating (Left–Right positions) — What is R's position from the left end in a row? Statements: I. M is tenth from the left end of the row. II. There are sixteen children between M and R.

Difficulty: Medium

Statement I alone is sufficient; Statement II alone is not sufficient.
Statement II alone is sufficient; Statement I alone is not sufficient.
Either Statement I alone or Statement II alone is sufficient.
Both Statements I and II together are not sufficient.
Both Statements I and II together are sufficient, but neither alone is sufficient.

Correct Answer: Both Statements I and II together are sufficient, but neither alone is sufficient.

Explanation:

Introduction / Context:
We must find R's exact position from the left end using relative placement information. Data Sufficiency (DS) requires checking if a unique answer is implied without assuming missing facts like total class size unless forced by logic.

Given Data / Assumptions:

I: M is 10th from the left.
II: There are 16 children between M and R.
Positions are whole numbers; a person cannot be at position ≤ 0.

Concept / Approach:
Translate the 'k between' language into a fixed offset of k+1 places to the left or right. Validate side choices against boundary feasibility.

Step-by-Step Solution:

From I alone: R's position is unknown; we only know M = 10th.From II alone: Only the gap between M and R is known (16 between), but neither absolute side nor any anchor position is given.Combine I & II: If R is to the right of M, then R = 10 + 16 + 1 = 27th. If R is to the left, R = 10 − 16 − 1 = −7 (impossible). Hence only the right-side placement is valid ⇒ R is 27th from the left.

Verification / Alternative check:
We do not need the row length; the invalid negative index eliminates the left-side case, leaving a unique feasible position.

Why Other Options Are Wrong:

A/B/C: Each single statement lacks enough information.
D: Incorrect, because together they yield a single valid position.

Common Pitfalls:
Forgetting to add +1 when converting 'k between' to the actual offset; overlooking boundary invalidation on the left side.

Final Answer:
E — Together sufficient (R is 27th from the left).

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Seating (Left–Right positions) — What is R's position from the left end in a row? Statements: I. M is tenth from the left end of the row. II. There are sixteen children between M and R.

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