Question

A new number is formed by interchanging the digits of a two-digit number. So the difference of those two numbers will be divisible by which number?

a) 2
b) 5
c) 9
d) 11

Answer 1

Answer: D

Step-by-step explanation: lol just guessing

Answer 2

The difference of the two numbers will always be divisible by 9. Option C is correct.

Step-by-step explanation:

When we interchange the digits of a two-digit number, the resulting number will be greater than the original number if the tens digit is larger than the units digit, and vice versa. Let's consider two cases:

If the tens digit is larger than the units digit, the resulting number will be greater than the original number. The difference between the resulting number and the original number will be positive. For example, if the original number is 17 and we interchange the digits, the resulting number will be 71. The difference is 71 - 17 = 54, which is divisible by 9.

If the units digit is larger than the tens digit, the resulting number will be smaller than the original number. The difference between the resulting number and the original number will be negative. For example, if the original number is 71 and we interchange the digits, the resulting number will be 17. The difference is 17 - 71 = -54, which is also divisible by 9.

Therefore, the difference of the two numbers will always be divisible by 9.