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

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Solution

The correct option is B 3
The numbers can be written as:

$a b c = 100 a + 10 b + c$

$c a b = 100 c + 10 a + b$

$b c a = 100 b + 10 c + a$

Adding all we get;

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

Sum
$= 111 a + 111 b + 111 c$

Sum
$= 111 (a + b + c)$

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

$∴$ the the number will be divisible by 3.

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