Difficulty: Easy
Correct Answer: 11
Explanation:
Introduction / Context:
This question tests basic average and total calculation skills. When some subgroup averages are known, we can calculate their total contributions and isolate the missing individual value.
Given Data / Assumptions:
- Number of students = 15.
- Overall average age = 15 years.
- Average age of 5 students = 14 years.
- Average age of another 9 students = 16 years.
- All ages are in years.
Concept / Approach:
From the average we find total age as:
Total age = Average age * Number of students
We compute the total age of the known subgroups and subtract from the overall total to get the age of the remaining student.
Step-by-Step Solution:
Step 1: Total age of all 15 students = 15 * 15 = 225 years.Step 2: Total age of the 5 students = 14 * 5 = 70 years.Step 3: Total age of the 9 students = 16 * 9 = 144 years.Step 4: Combined age of these 14 students = 70 + 144 = 214 years.Step 5: Age of the remaining one student = Total age - Combined age of 14 students.Step 6: Age of the fifteenth student = 225 - 214 = 11 years.
Verification / Alternative check:
Check by recomputing the average: the 14 known students contribute 214 years plus the remaining 11 years gives 225 years. Dividing 225 by 15 returns 15, which matches the given overall average, confirming that 11 years is correct.
Why Other Options Are Wrong:
- 12, 13 and 14 years would give totals of 226, 227 and 228 respectively, leading to averages higher than 15 years.
- These values conflict with the given overall average when checked through recomputation.
Common Pitfalls:
- Forgetting that 5 + 9 = 14 students, not 15, and mistakenly using 10 or 9 as the remaining count.
- Computing the averages but not converting them into totals, which is necessary to isolate the missing value.
Final Answer:
The age of the fifteenth student is 11 years.
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