NMOS 2010 Q19

Q19. A, B and C are letters that represent different odd digits such that ABC is a 3-digit number. If ABC is a multiple of A, B and C , how many different 3-digit numbers ABC are there?


ABC = A x = B x = C x


A, B, C – odd digits

Odd digits – 1, 3, 5, 7, 9


5 x 4 x 3 = 60 different numbers



Numbers that meet the above conditions are


135 = 1 x 135, 3 x 45, 5 x 27


175 = 1 x 175, 7 x 25, 5 x 35


315 = 3 x 105, 1 x 315, 5 x 63


735 = 7 x 105, 3 x 245, 5 x 147



There are 4 different 3-digit numbers.