Question

The sum of all three-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11 is

Answer 1

Such numbers are 11 x 19, 11 x 20, 11 x 22, 11 x 23,....., 11 x 28, 11 x 30, 11 x 32,....., 11 x 37, 11 x 39, 11 x 40, 11 x 42,.....,11 x 45

Sum = 11 (19 + ..... + 45 - 21 - 29 - 31 - 38 - 41)

= 11 (1 + ..... + 45 - 160 - (1 + 2 + 3 + ..... + 18))

= 11 (1035 - 160 - 171)

= 11 x 704

= 7744