Multiple choice

A student types a number using the first 100 natural numbers from left to right as 1234567891011121314…99100. Find the remainder when this number is divided by 9.

  1. 0

  2. 1

  3. 2

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. The number is formed by concatenating 1 to 100. The sum of digits of numbers 1-99 can be found by pairing (0,99), (1,98)...(49,50), each pair summing to 18, plus the digits of 100. The total sum of digits is 901. 901 mod 9 = 1.

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