Multiple choice

The sum of the digits of a four-digit number is 31. What fraction of such numbers are divisible by 11?

  1. 14

  2. 15

  3. 16

  4. None of these

  5. 13
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D Correct answer
Explanation

For divisibility by 11, the difference between the sums of alternating digits must be a multiple of 11. With total digit sum 31, the required alternating sums would be 21 and 10, but an alternating sum of 21 is impossible for two digits. Therefore, the fraction is 0, which is not listed.

AI explanation

For a four-digit number to have a digit sum of 31, it must consist of four 9s and one 7. This gives 4 possible combinations where the 7 is in one of the four digit positions: 7999, 9799, 9979 and 9997. Testing these, none of the 4 numbers are divisible by 11; therefore, 0 out of 4 are divisible by 11, meaning the answer is none of these.

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