Multiple choice

How many two-digit numbers will give a remainder of 1, when divided by 3 and a remainder of 3, when divided by 4?

  1. 4

  2. 5

  3. 6

  4. 7

  5. 8

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D Correct answer
AI explanation

Let the two-digit number be N, which means it can be expressed as 3x + 1 and 4y + 3. Solving the congruence N modulo 3 equals 1 and N modulo 4 equals 3 yields a general form of N = 12k + 7. For two-digit numbers, substituting integer values for k from 1 through 7 produces the valid numbers 19, 31, 43, 55, 67, 79 and 91, giving a total of 7 such numbers.