Multiple choice

A 4-digit positive number and a 3-digit positive number, when divided by 4, 5, 6 or 7, always leave a remainder of 3. What is the difference between such smallest 4-digit number and the largest 3-digit number?

  1. 420

  2. 517

  3. 400

  4. 4

  5. 840
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A Correct answer
Explanation

The number must be of the form LCM(4,5,6,7)*k + 3. LCM(4,5,6,7) = 420. Smallest 4-digit number of this form is 420*3 + 3 = 1263. Largest 3-digit number of this form is 420*2 + 3 = 843. Difference = 1263 - 843 = 420.

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