Data Sufficiency – Positions in a Row Question: What is Sumit’s position from the right end in a row of children? Statements: I. There are 10 children between Sumit and Rajan. II. Rajan is 20th from the left end of the row.

Introduction / Context:
This Data Sufficiency question concerns linear arrangement indices. We are asked for Sumit’s position from the right end, which requires both his absolute position and the total number of children (or an equivalent piece of information).

Given Data / Assumptions:

• I: Exactly 10 children lie between Sumit and Rajan.
• II: Rajan is 20th from the left end.
• Total number of children in the row is not directly given.

Concept / Approach:
Knowing a gap between two persons plus one absolute position can still leave two possible positions for the other person (to the left or to the right), unless additional constraints or boundaries are given. To find a position from the right, we typically also need the total count or a right-end reference.

Step-by-Step Reasoning:
From II: Rajan = 20th from the left. From I: Sumit is either 11 places to the right of Rajan or 11 places to the left of Rajan (since 10 in between implies a separation of 11 positions). Thus Sumit could be either 31st from the left or 9th from the left. Without the total number of children, Sumit’s position from the right remains undetermined in both cases.

Verification / Alternative check:
Even combining I and II, we do not know the total size of the row. Two distinct possibilities remain, giving different answers from the right end.

Why Other Options Are Wrong:
'I alone' or 'II alone': Each is clearly insufficient. 'Either' or 'Both': Incorrect, because ambiguity persists without row length.

Common Pitfalls:
Assuming the person must be to one specific side without justification. Forgetting that 'from the right' demands knowing the total count.

Final Answer:
Neither I nor II is sufficient