Multiple choice

Consider the following number: 301K472M. Both 'K' and 'M' represent single-digit integers from 0 to 9. How many possible pairs of 'K' and 'M' are possible for which the number is divisible by 11, and when divided by 9, the remainder is 2?

  1. 1

  2. 3

  3. 4

  4. No such values of K and M are possible.

  5. a
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C Correct answer
AI explanation

For the number 301K472M to leave a remainder of 2 when divided by 9, the sum of its digits minus 2 must be a multiple of 9, leading to K plus M equals 7. For divisibility by 11, the difference between the sum of alternating digits must be a multiple of 11, giving the equation M minus K minus 4 equals 0 or 11. Solving these two conditions yields four valid single-digit pairs for (K, M): (0, 7), (1, 6), (2, 5), and (3, 4). Therefore, there are 4 possible pairs.

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