Averages — “The average age of friends A, B, and C is 20. The average of A and B alone is 19. What is C’s age?”
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A20 years
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B21 years
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C22 years
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D24 years
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E18 years
Answer
Correct Answer: 22 years
Explanation
Introduction / Context:Comparing the totals from two averages (three-person average vs. two-person average) isolates the third person’s value directly. This is a standard averages technique.
Given Data / Assumptions:
- average(A,B,C) = 20 ⇒ sum(A,B,C) = 60.
- average(A,B) = 19 ⇒ sum(A,B) = 38.
- C = sum(ABC) − sum(AB).
Concept / Approach:Compute both sums and subtract to get C’s age without solving for A or B individually.
Step-by-Step Solution:
sum(ABC) = 3 * 20 = 60.sum(AB) = 2 * 19 = 38.C = 60 − 38 = 22 years.Verification / Alternative check:If A + B = 38 and C = 22, then the average over three is (38 + 22)/3 = 60/3 = 20, matching the given condition.
Why Other Options Are Wrong:18/20/21/24 do not equal the required difference of totals.
Common Pitfalls:Trying to assume A = B; or averaging the two averages directly instead of converting to totals first.
Final Answer:22 years