Multiple choice

If we divide the sum of first 100 numbers by 9, then what is the remainder?

  1. 8

  2. 7

  3. 5

  4. 1

  5. 0
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D Correct answer
Explanation

Sum of first n numbers = n(n+1)/2. For n=100, Sum = 100 * 101 / 2 = 5050. 5050 divided by 9: 5050 = 9 * 561 + 1. The remainder is 1.

AI explanation

Using the formula for the sum of the first n natural numbers, the sum of the first 100 numbers is 100 times 101 divided by 2, which gives 5050. To find the remainder when 5050 is divided by 9, we apply the divisibility rule for 9 and add the digits of 5050. The sum of the digits is 5 + 0 + 5 + 0 = 10. When 10 is divided by 9, the remainder is 1.

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