Let abc be a three-digit number.

Question:

 Let abc be a three-digit number. Then, abc – cba is not divisible by

(a) 9

(b) 11

(c) 18

(d) 33

Solution:

(c) Given, abc is a three-digit number.

Then, abc = 100a + 10b + c

and cba = 100c + 10b + a

abc -eba = (100a + 10b + c)- (100c + 10b + a)

= 100a – a + 10b – 10b + c -100=

= 99a – 99c = 99 (a -c)

= abc-cba is divisible by 99.

=> abc – cba is divisible by 9,11,33, but it is not divisible by 18.

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