Multiple choice

Find the greatest number of four digits which when divided by 10, 11, 15 and 22 leaves 3, 4, 8 and 15 as remainders, respectively.

  1. 9907

  2. 9903

  3. 9893

  4. 9993
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C Correct answer
Explanation

The differences between divisors and remainders are (10-3)=7, (11-4)=7, (15-8)=7, (22-15)=7. Find LCM(10, 11, 15, 22) = 330. The largest 4-digit number is 9999. 9999 / 330 = 30 with remainder 99. The largest multiple is 9999 - 99 = 9900. Subtracting the common difference 7, we get 9900 - 7 = 9893.

AI explanation

Observe that the difference between each divisor and its respective remainder is exactly 7. This means if you add 7 to the unknown number, it becomes a common multiple of 10, 11, 15, and 22. The least common multiple of these divisors is 330. The greatest four-digit multiple of 330 is 9900, and subtracting 7 gives the final result of 9893.

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