If abc is a three digit number, then the number abc – a – b – c is divisible by

Question

Philoid · Accepted Answer

Since abc is a three digit number

∴ General form of abc is abc = 100a + 10b + c

Now; abc – a – b – c = 100a + 10b + c – a – b – c.

⇒ abc – a – b – c = 100a – a + 10b – b + c – c.

⇒ abc – a – b – c = 99a + 9b.

⇒ abc – a – b – c = 9( 11a + b).

∴ abc – a – b – c is divisible by 9 because 9 is one of its factor.

Hence the correct option is (a).