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?”

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:

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