Question

The sum of a three digit number and the number formed by the reversal of its digits (if for both the numbers middle digit is 0) is always divisible by 101

• A. True
• B. False

Answer 1

The correct option is A

True

Let abc be the number.
Thus abc = 100a + 10b + c
The number obtained by reversing the digits is cba.
cba = 100c + 10b + a

Adding the two numbers we get, abc + cba = (100a + 10b + c) + (100c + 10b + a) = 101a + 20b + 101c

Since middle digit is 0, the sum will be 101(a+c), which is divisible by 101.