Question

If all students passed the exam, and some students are athletes, which of the following must be true?

• A. All athletes passed the exam.
• B. Some athletes failed the exam.
• C. No athletes passed the exam.
• D. Some students are not athletes.
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Hint:

In critical reasoning questions, ensure the conclusion is necessitated by the premises, not just possible. Use subset relationships to deduce what must be true.

Answer 1

The Correct Option is A

- Step 1: Break down the premises. The question provides two premises:
- Premise 1: All students passed the exam (every student passed).
- Premise 2: Some students are athletes (at least one student is an athlete).
- Step 2: Analyze logical implications. Since some students are athletes, and all students passed the exam, the athletes who are students must also have passed the exam. If all athletes in the context are students, they all passed.
- Step 3: Evaluate the options.
- Option (1): "All athletes passed the exam" is true, as the athletes who are students (from premise 2) must have passed (from premise 1), assuming all relevant athletes are students.
- Option (2): "Some athletes failed the exam" contradicts premise 1, as all students (including athlete-students) passed.
- Option (3): "No athletes passed the exam" also contradicts premise 1, as athlete-students passed.
- Option (4): "Some students are not athletes" is possible but not necessarily true, as the premises do not confirm non-athlete students.
- Step 4: Confirm with a Venn diagram. Imagine students as a circle where all passed the exam, with athletes as a smaller circle inside (some students are athletes). All within the student circle passed, including athletes.
- Step 5: Address assumptions. The question implies athletes are within the student group, as no non-student athletes are mentioned. Thus, all relevant athletes passed.
- Step 6: Final conclusion. Option (1) All athletes passed the exam is the correct answer, as it logically follows from the premises.
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