Question

If the sum of three consecutive integers is less than 75, find the cube of the largest possible integer.

Answer 1

The cube of the largest number is < 19683

Explanation:

let the three integers be :- x, x+1, x+2

x + (x+1) + (x+2) < 75 (given)

x + x + x + 1 + 2 = 75 (considering that the sum is 75)

3x + 3 = 75

3(x + 1) = 75

x + 1 = 75/3 = 25

x = 24

The largest number is x + 3

x + 3 = 27

(x + 3)^3 = 27^3

= 19683