Five friends- Aka, Bka, Cka, Dka and Eka are sitting in a row. Among all who…

Concept: In a data-sufficiency question, the correct combination is the SMALLEST set of statements that, together, fixes exactly one answer to the question asked. A larger set that still works is not the intended answer if a smaller subset within it already determines the answer on its own — the larger set is then treating redundant information as necessary. Throughout, "X is between Y and Z" means X sits directly adjacent to both Y and Z — the standard reading for a fixed row of exactly the five named people.

Application: Test every combination of statements.

1. Statement I: Bka is between Eka and Cka, so these three sit as one block, but the direction is not fixed — it could be Eka, Bka, Cka or Cka, Bka, Eka.

2. Statement III: Dka is between Aka and Eka, so these three sit as one block, direction also not fixed — it could be Aka, Dka, Eka or Eka, Dka, Aka.

3. Combine Statement I with Statement III alone (without Statement II): the two blocks share Eka, and they can only merge without a seat clash in two ways — Eka-Bka-Cka extending right of Eka with Aka-Dka-Eka extending left of Eka gives Aka, Dka, Eka, Bka, Cka; or Cka-Bka-Eka extending left of Eka with Eka-Dka-Aka extending right of Eka gives Cka, Bka, Eka, Dka, Aka. In BOTH of these valid rows, Eka sits in the middle (3rd) seat.

4. Since every arrangement consistent with Statements I and III alone puts Eka in the middle, these two statements together already answer the question fully — Statement II is not needed to fix who sits in the middle.

5. Check Statements I and II alone (without III): they fix only the block Eka, Bka, Cka in that direction, but say nothing about where Aka and Dka sit. That block could occupy seats 1-3, 2-4, or 3-5 of the row, and each placement puts a different friend in the middle seat — insufficient.

6. Check Statements II and III alone (without I): Statement II only places Bka to the right of Eka without fixing adjacency to Cka, and Statement III's block direction is still open. More than one seating survives, so the middle occupant cannot be pinned down — insufficient.

Cross-check: The two rows consistent with Statements I and III alone — Aka, Dka, Eka, Bka, Cka and Cka, Bka, Eka, Dka, Aka — both place Eka third of five. So Statements I and III together are both necessary and sufficient to answer who sits in the middle; adding Statement II is redundant, and no smaller pair (I&II, or II&III) works on its own.