Question

Take a 3 digit number 'abc'. If we add abc, cab and bca together then the resulting sum is divisible by:

• A. 11
• B. 111
• C. 37
• D. 111 and 37

Answer 1

Answer: (B), (C), (D)

The correct options are
B

111

C

37

D

111 and 37

The numbers can be written as:

abc = 100a + 10b + c

cab = 100c + 10a + b

bca = 100b + 10c + a

Adding all we get

Sum = (100a + 10a + a) + (100b + 10b + b) + (100c + 10c + c)

Sum = 111a + 111b + 111c

Sum = 111 (a + b + c)

= 37 $\times$ 3 (a + b + c)

$\frac{sum}{111}$ = (a + b + c)

$\frac{sum}{37}$= 3 (a + b + c)

Therefore, the number will be divisible by 111, 37, 3 and (a + b + c).