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 only of 1s is 111,111,111.
There is a specific mathematical pattern when numbers made of only the digit 1 are squared. For example: 1 squared is 1. Sum of digits is 1. 11 squared is 121. Sum of digits is 4. 111 squared is 12,321. Sum of digits is 9.
The pattern shows that the result of squaring a number with n ones is a palindrome that increases from 1 up to n and then decreases back to 1.
For a 9 digit number of 1s, the result of the multiplication is 123,456,789,876,543,210. Wait, a simpler way to find the sum of digits is to realize that for any number n where n is less than or equal to 9, the sum of the digits of the square of a number consisting of n ones is simply n squared.
Since there are 9 ones in this number, the sum of the digits of the result is 9 squared, which equals 81.
Therefore, the correct option is C.
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