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.

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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

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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.

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

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