Question

Statement: All the students passed the examination. Some students are girls ? Conclusion: (1)Some boys passed the Examination (2)All the girls failed the Examination (3)None of the boys passed the Examination (4) None of the girls failed in the Examination

• A. 1 and 2 follow
• B. 2 and 3 follow
• C. 1 and 2 and 3 follow
• D. none of the above

Answer 1

Answer:

D. none of the above

The correct conclusion is (4) None of the girls failed in the Examination.

1. Analyze Statement 1: "All the students passed the examination."
   This means that the failure rate for any student in the group is exactly 0%. No student failed.

2. Analyze Statement 2: "Some students are girls."
   This establishes that girls are a part of the student group.

3. Combine the Statements: Since all students passed the exam, and girls are a subset of these students, it means every single girl passed the examination. Therefore, no girls could have failed.

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• ❌ (1) Some boys passed the Examination: The statements only tell us that some students are girls. We do not have explicit information confirming that the remaining students are boys (they could theoretically all be girls, or include other groups), so we cannot definitively conclude this.

• ❌ (2) All the girls failed the Examination: This directly contradicts the first statement that all students passed.

• ❌ (3) None of the boys passed the Examination: Similar to option 1, we cannot make a definitive conclusion about boys since the prompt does not explicitly mention them or define the remaining student population.

• (4) None of the girls failed in the Examination: This is completely true and logically certain. Because 100% of the students passed, 100% of the girls passed, leaving 0% of the girls failed.