Multiple choice

The numbers 1 to 29 are written side by side as follows to obtain a single number. 1 2 3 4 5 6 7 8 9 ... 27 28 29. If the number is divided by 9, then what will be the remainder?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 6
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D Correct answer
Explanation

A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of digits from 1 to 29: Sum of digits 1-9 = 45. Sum of digits 10-19 = (1*10) + 45 = 55. Sum of digits 20-29 = (2*10) + 45 = 65. Total sum = 45 + 55 + 65 = 165. 165 / 9 = 18 with a remainder of 3.

AI explanation

Using the divisibility rule for 9, the remainder of a number divided by 9 is the same as the remainder of the sum of its digits divided by 9. We find the sum of the numbers from 1 to 29 using the formula n times n plus 1 divided by 2, which gives 29 times 30 divided by 2, equaling 435. The sum of the digits of 435 is 4 plus 3 plus 5, which equals 12. Dividing 12 by 9 leaves a remainder of 3.

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