Multiple choice

Which of the following could be remainders when five consecutive positive integers are divided by 4?

  1. 0, 1, 2, 3

  2. 1, 2, 3

  3. 0, 1, 2, 3, 4

  4. 1, 2, 3, 4

  5. 0, 1, 3, 4, 5
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A Correct answer
Explanation

When any integer is divided by 4, the possible remainders are 0, 1, 2, and 3. Five consecutive integers will cycle through these remainders.

AI explanation

When consecutive positive integers are divided by 4, their remainders must form a consecutive sequence that cycles through the possible remainders. The only possible remainders when dividing by 4 are 0, 1, 2 and 3. Because dividing by 4 never produces a remainder of 4, options containing 4 or 5 are incorrect. Since any five consecutive integers will cover at least the four distinct remainders 0, 1, 2 and 3, the set of remainders must be 0, 1, 2, 3.

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