The arithmetic mean of five different natural numbers is 12. The largest possible value among the numbers is A. 12 B. 40 C. 50 D. 60

GATE 2012 · General Aptitude · Statistics · medium

Answer: The largest possible value is 50 (Option C).

1. Compute the total sum from the mean: Sum = 12 x 5 = 60. All five different natural numbers must add up to 60.
2. Minimize the four smaller numbers: The four smallest distinct natural numbers are 1, 2, 3, 4. Their sum = 1 + 2 + 3 + 4 = 10.
3. Calculate the maximum fifth number: Largest = 60 - 10 = 50. Verify: {1, 2, 3, 4, 50} are five different natural numbers with mean (1+2+3+4+50)/5 = 60/5 = 12. Check all are distinct: yes.