Average age application: The average of A, B, C, D, and E is 40 years. The average of A and B is 35 years, and the average of C and D is 42 years. Find the exact age of E.

Introduction / Context:
This problem tests the ability to manipulate averages by converting them into total sums. When multiple subgroup averages are given, convert each to totals and combine to isolate the missing value.

Given Data / Assumptions:

• Average of A, B, C, D, E = 40 years
• Average of A and B = 35 years
• Average of C and D = 42 years

Concept / Approach:
Average * count = total. Sum all five, subtract the totals of the two given pairs, and what remains is the age of E.

Step-by-Step Solution:

Verification / Alternative check:
Distribute values: If A + B = 70 and C + D = 84, then these four together are 154. The overall of five is 200. The leftover 46 must be E.

Why Other Options Are Wrong:

• 48, 44, 40: incorrect subtractions from the total.
• 32: likely from mixing up averages with totals.

Common Pitfalls:
Forgetting to multiply averages by the correct count or mixing up addition and subtraction when isolating the unknown.

Final Answer:
46 years