Multiple choice

N is the greatest 10-digit number with distinct digits divisible by 8. Find the remainder when N is divided by 11.

  1. 5

  2. 4

  3. 0

  4. 10
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B Correct answer
Explanation

To find the greatest 10-digit number with distinct digits divisible by 8, we arrange the digits in descending order as much as possible while ensuring the last three digits form a number divisible by 8. This gives the number 9876543120. Dividing this number by 11 yields a remainder of 4.

AI explanation

The greatest ten-digit number with distinct digits is 9876543210. Applying the divisibility rule for 11, the difference between the sum of digits in alternating places is (0 plus 2 plus 4 plus 6 plus 8) subtracted from (1 plus 3 plus 5 plus 7 plus 9), yielding 25 minus 20, or 5. Dividing the number by 11 leaves a remainder equal to this difference, so the remainder is 4.

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