The number of 3 -digit odd numbers, whose sum of digits is a multiple of 7 , is _____.

Step-by-step solution

Let the three-digit odd number be x y z Now z = 1 / 3 / 5 / 7 / 9 x + y + z = 7 / 14 / 21 [for sum of digit to be multiple of 7 ] x + y   = 6 / 4 / 2 / 13 / 11 / 9 / 7 / 5 / 20 / 18 / 16 / 14 / 12 When x + y = 6 ⇒ 1 , 5 , 2 , 4 , 3 , 3 , 4 , 2 , 5 , 1 , 6 , 0 Total possibilities = 6 When x + y = 4 ⇒ 1 , 3 , 2 , 2 , 3 , 1 , 4 , 0 Total possibilities = 4 When x + y = 2 ⇒ 1 , 1 , 2 , 0 Total possibilities = 2 When x + y = 13 ⇒ 4 , 9 , 5 , 8 , 6 , 7 , 7 , 6 , 8 , 5 , 9 , 4 Total possibiliti