Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?
- A64
- B80
- C81Correct
- D100
Explanation
The 9 digit number consisting of all 1s is 111,111,111. When a number consisting only of the digit 1 is squared, the result follows a specific mathematical pattern.
For example: 1 squared is 1. Sum of digits is 1. 11 squared is 121. Sum of digits is 1 plus 2 plus 1 which is 4. 111 squared is 12321. Sum of digits is 1 plus 2 plus 3 plus 2 plus 1 which is 9.
The pattern shows that the sum of the digits of the square is always the square of the number of digits in the original number. In this case, the original number has 9 digits. Therefore, the sum of the digits of the resulting number is 9 squared, which equals 81.
The resulting number itself is 12,345,678,987,654,321. Adding these digits together also gives 81.
The correct answer is C.
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