Question

Question 4

In the given question, out of four options, only one is correct. Write the correct answer.

Let abc be a three-digit number. Then, abc - cba is not divisible by
(a) 9
(b) 11
(c) 18
(d) 33

Answer 1

Given, abc is a three-digit number.
Then, abc = 100a + 10b + c
and cba = 100c + 10b + a
$\therefore$ abc - cba = (100a + 10b + c) - (100c + 10b + a)
= 100a - a + 10b - 10b + c - 100c
= 99a - 99c = 99 (a - c)
$\Rightarrow$ abc - cba is divisible by 99.
$\Rightarrow$ abc - cba is divisible by 9, 11, 33, but it is not divisible by 18.