In a school there are three batches of players who play cricket, football and hockey. An incomplete chart of number of students playing an individual sport belonging to an individual batch is displayed in the following table: Cricket players — Batch I: 8, Total: 14; Football players — Batch II: 10, Total: 16; Hockey players — Batch I: 6, Batch III: 6, Total: 17. Which one of the following is correct?
- ABatch II is empty
- BBatch I and Batch II do not have equal number of students
- CBatch I and Batch III can have equal number of students
- DBatch II and Batch III can have equal number of students
Explanation
Hockey gives Batch II = 17 - 6 - 6 = 5 players, so Batch II is not empty and (A) is false. Let cricket be split C1 + C2 = 6 and football F1 + F2 = 6 across Batches I and II; Batch I totals C1 + F1 + 6 and Batch II totals C2 + F2 + 5. Equality would require 2(C1 + F1) = 11, impossible for integers, so the batches necessarily differ and (B) is correct. Batch III totals 8 + 10 + 6 = 24, which exceeds the maximum attainable Batch I (18) or Batch II (17), so (C) and (D) are false.