Class average with subgroup averages: Average age of 9 students and their teacher (10 persons) is 16 years. The first four students average 19 years; the last five average 10 years. Find the teacher’s present age.
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
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A36 yr
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B34 yr
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C30 yr
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D28 yr
Answer
Correct Answer: 34 yr
Explanation
Introduction / Context:Averages in parts (subgroups) and a grand average allow reconstruction of the missing individual’s value by total-sum arithmetic.
Given Data / Assumptions:
- Total persons = 10 (9 students + 1 teacher); grand average = 16.
- First 4 students average = 19; last 5 students average = 10.
Concept / Approach:Compute totals for each group, sum them to get students’ total, subtract from the grand total to isolate the teacher’s age.
Step-by-Step Solution:
Grand total = 10 * 16 = 160.First four total = 4 * 19 = 76.Last five total = 5 * 10 = 50.All students total = 76 + 50 = 126.Teacher = 160 − 126 = 34.Verification / Alternative check:
Totals reconcile exactly to the grand average.Why Other Options Are Wrong:
- 36, 30, 28 do not match the computed total balance.
Common Pitfalls:
- Forgetting that 9 students + teacher = 10 persons for the grand average.
Final Answer:34 yr