Question

A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by which of the following:
(a) 3
(b) 5
(c) 9
(d) 11

Answer 1

Hint: For the original number, let the digit in the units place be y and the digit in the tens place be x. Using this, the original number is 10x + y. On exchanging the digits, the new number becomes 10y + x. Add these two numbers and check their sum’s divisibility by the numbers given in the options.

Complete step-by-step answer:
In this question, we are given that a number consists of two digits. If the digits interchange places and the new number is added to the original number.
We need to find that the resulting number is divisible by which number in the options.
For the original number, let the digit in the units place be y and the digit in the tens place be x.
Using this, the original number is 10x + y.
Now, when we interchange the digits, for the new number, the digit in the units place is x and the digit in the tens place is y.
Using this, the new number is 10y + x.
Now, we will add these numbers to get the resultant number.
(10x + y) + (10y + x) = 11(x + y)
Clearly, the resultant number is divisible by 11 which is in the options.
So, option (d) is correct.

Note: In this question, it is very important to understand the meaning of the question and then form the two numbers using two variables properly. If you commit mistakes in this step, you will end up making mistakes and get the wrong answer.