Statement: In a one day cricket match, the total runs made by a team were 200.
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Statement:** In a one day cricket match, the total runs made by a team were 200. Out of these, 160 runs were made by spinners.
Conclusions:
I. 80% of the team consists of spinners.
II. The opening batsmen were spinners.
Which of the conclusions logically follow?
Show answer & explanation
Conclusion I conflates runs scored with team composition—160/200 = 80% of runs, not 80% of players. A few spinners could have scored all 160 runs while most of the team are batsmen. Conclusion II makes an unfounded assumption about opening batsmen with no supporting evidence in the statement. Neither conclusion logically follows from the given data.
Step-by-step Derivation:
Statement analysis:
- Total runs: 200
- Runs by spinners: 160
- Percentage of runs by spinners: 160/200 = 80%
Conclusion I evaluation:
- The statement says 80% of runs came from spinners, not that 80% of the team are spinners.
- Example: 2 spinners could score 160 runs; 9 batsmen could score 40 runs. Team composition = 2/11 ≈ 18% spinners, not 80%.
- Confuses performance (runs) with composition (number of players).
- Does NOT follow.
Conclusion II evaluation:
- The statement provides no information about batting order, opening positions, or specific player roles.
- No logical connection between total runs by spinners and who batted first.
- Does NOT follow.
Answer: D (Neither I nor II follows)