The product of three consecutive numbers when divided by each of them in turn gives three quotients. The sum of these three quotients is equal to 74.

What are the numbers ?

Let the number be n-1, n & n+1.

Then, n = sqrt{(∑Q + 1) / 3) always.

In this case ∑Q = 74.

Hence n = sqrt{74 + 1) / 3) = sqrt (75/3) = sqrt(25) = ±5.

Hence the numbers are 4,5,6 OR -6,-5,-4