Question:
Let abc be a three-digit number. Then, abc + bca + cab is not divisible by
(a) a + b + c
(b) 3
(c) 37
(d) 9
Solution:
(d) We know that, the sum of three-digit numbers taken in cyclic order can be written as 111 (a + b + c).
i.e. abc + pea + cab = 3 x 37 x (a + b + c)
Hence, the sum is divisible by 3, 37 and (a + b + c) but not divisible by 9.