2025 · Q61
Three distinct positive integers a, b and c are such that b-a = c-b and a+b+c = 12. What is the maximum number of such possible sets (a, b, c)?
General Mental Ability, Quantitative Aptitude and StatisticsNumber system
- A1
- B2
- C3
- D4
Explanation
Since a, b, c are in arithmetic progression with sum 12, 3b = 12 so b = 4, and a + c = 8. With distinct positive integers and a < 4 < c, the possibilities are (1,4,7), (2,4,6) and (3,4,5), i.e. 3 sets. No other triple satisfies all conditions.