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The digits indicated by * in 3422213** so that this number is divisible by 99 areOptions1,93,74,65,5

Question

The digits indicated by * in 3422213** so that this number is divisible by 99 are Options 1, 93, 74, 65, 5.

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Solution

To find the digits that make the number 3422213** divisible by 99, we need to understand the divisibility rule for 99. A number is divisible by 99 if it is divisible by both 9 and 11.

  1. Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9. Let's add the digits of the number 3422213**: 3+4+2+2+2+1+3 = 17. To make the sum divisible by 9, the sum of the two missing digits should be 9 - (17 mod 9) = 1. So, the sum of the two missing digits should be 1.

  2. Divisibility rule for 11: A number is divisible by 11 if the difference between the sum of digits at odd places and the sum of digits at even places is either 0 or a number divisible by 11. Let's calculate the difference for the number 3422213**: Sum of digits at odd places = 3+2+2+3 = 10. Sum of digits at even places = 4+2+1 = 7. The difference is 10 - 7 = 3. To make the number divisible by 11, the difference between the sum of the two missing digits and 3 should be a multiple of 11. Since the sum of the two missing digits is 1, the only way to achieve this is if one of the digits is 0 and the other is 1.

So, the digits that make the number 3422213** divisible by 99 are 0 and 1. However, the order of these digits depends on their placement. If the first missing digit is at an odd place, then the first digit should be 1 and the second digit should be 0. If the first missing digit is at an even place, then the first digit should be 0 and the second digit should be 1.

Looking at the options, the correct answer is not listed.

This problem has been solved

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