Multiple choice general knowledge math & puzzles

in a series 1 is repeated once 2 is repeated twice 3 is repeated thrice and so on what would be the digit when sum of all digit reaches 300?

  1. 1

  2. 2

  3. 3

  4. 4
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A Correct answer
Explanation

The series is: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, ... We sum digits sequentially: 1 (sum=1), 2+2=4 (sum=5), 3+3+3=9 (sum=14), 4x4=16 (sum=30), 5x5=25 (sum=55), 6x6=36 (sum=91), 7x7=49 (sum=140), 8x8=64 (sum=204), 9x9=81 (sum=285), then we need 15 more. The next digits are 1, 1, 1,... and 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 15. So the 300th digit is 1.

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