Multiple choice

Find the greatest four-digit number which is perfectly divisible by 3 and when divided by 5, 7 or 9, leaves a remainder 3.

  1. 9453

  2. 9762

  3. 9768

  4. 9775
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C Correct answer
Explanation

The number must be divisible by 3. Also, N = LCM(5, 7, 9) * k + 3 = 315k + 3. We check multiples of 315 plus 3 that are divisible by 3. 315k + 3 is always divisible by 3. We want the largest 4-digit number: 315k + 3 <= 9999 => 315k <= 9996 => k <= 31.7. For k=31, N = 315*31 + 3 = 9765 + 3 = 9768.

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