2026 · Q37
All possible groups of 3 distinct numbers from among A, B, C, D and E are formed. If the aggregate of sums of numbers of each group is 120, then what is the arithmetic mean of A, B, C, D and E?
Elementary MathematicsStatistics
- A4
- B5
- C10
- D20
Explanation
There are C(5,3)=10 groups of 3, and each of the five numbers occurs in C(4,2)=6 of them. The aggregate of the group sums is therefore 6(A+B+C+D+E)=120, so the total is 20 and the mean is 4, option A. The key insight is symmetry: each of the five numbers contributes equally to the aggregate sum.