Logical Reasoning – Categorical conclusions from match data: In a one-day cricket match, a team scored 200 runs, of which 160 runs were made by spinners. Which conclusion(s) follow logically? (I) 80% of the team members are spinners; (II) The opening batsmen were spinners.

Given data

• Total team runs = 200; runs by spinners = 160.
• Conclusions under test: (I) 80% of players are spinners; (II) Openers were spinners.

Concept/ApproachFrom aggregate runs by role, you cannot deduce player counts or batting order. Many runs can be made by a few spinners.

Step-by-step reasoning• 160/200 = 80% of runs, not 80% of players. Hence (I) is a scope error.• No information is provided about batting order; (II) is unwarranted.

Verification/AlternativeCounterexample: Two spinners score 160; the rest (non-spinners) score 40. Then players are not 80% spinners and openers may be non-spinners. Data still fits the premise.

Common pitfalls

• Confusing percentage of runs with percentage of players.
• Inferring order or roles not mentioned in the premise.

Final AnswerNeither I nor II follows.