There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers?
Answer & explanation
Answer: (a) 47
The mean of five consecutive odd numbers is the middle (third) one, so the third number is 39 and the list starts at 35. The mean of thirteen consecutive odd numbers is the 7th number: 35 + 6 × 2 = 47.
- Mean of 5 consecutive odd numbers = the 3rd number = 39, so the first number is 39 − 4 = 35.
- The 13 numbers are 35, 37, …, 59 (35 + 12 × 2 = 59), all 2-digit.
- Mean of an evenly spaced list = middle (7th) term = 35 + 6 × 2 = 47.
- Check: (35 + 59) ÷ 2 = 47.
Remember · For an evenly spaced list, the mean equals the middle term, or the average of the first and last terms.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·