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Question

Consider a 3-digit number and reverse its digits. Find the difference between original and reversed number. By what numbers this difference is divisible? Select all that apply.



A

9

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B

11

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C

5

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D

99

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Solution

The correct options are
A

9


B

11


D

99


Suppose abc be a 3-digit number.

Original number = 100a + 10b + c

Reversed number 100c + 10b + a

Difference = 100a + 10b + c - 100c - 10b - a

= 99a - 99c = 99(a - c)

The difference is divisible by 3, 9, 11, 33 and 99 


Mathematics

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