CSAT 2023

Q. 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?

(a) 64
(b) 80
(c) 81
(d) 100
Correct Answer: (c) 81

Question from UPSC Prelims 2023 CSAT

Explanation :

Each digit of a 9-digit number is 1

The 9-digit number with each digit as 1 is 111,111,111. When this number is multiplied by itself, the result is 12,345,678,987,654,321.

Sum of Digits Calculation
Now, if we sum up the digits of this number, we get:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 81.

Note: Pattern Formation:

11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = 1234321
11111 × 11111 = 123454321
111111 × 111111 = 12345654321 and so on…

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