The sum of three consecutive natural numbers each divisible by 3 is 72. What…

Solution: Let the three consecutive numbers divisible by 3 be 3n, 3(n+1), and 3(n+2).

Their sum is 3n + 3(n+1) + 3(n+2) = 9n + 9. Set this equal to 72:

9n + 9 = 72 ⇒ 9(n + 1) = 72 ⇒ n + 1 = 8 ⇒ n = 7.

So the three numbers are 3·7 = 21, 24, and 27. The largest is 27.

• Quick alternate method: the average of the three numbers is 72 ÷ 3 = 24, which is the middle number. Therefore the largest is 24 + 3 = 27.

Answer: 27