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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