Multiple choice

Find the least possible number when successively divided by 2, 5, 4 and 3 gives remainders 1, 1, 3 and 1 respectively.

  1. 60

  2. 72

  3. 73

  4. 75
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C Correct answer
Explanation

Work backwards from the last division. After dividing by 3, remainder 1, so N = 3a + 1. Before this, after dividing by 4, remainder 3, so 3a + 1 = 4b + 3, giving 3a = 4b + 2. Smallest solution: a = 2, b = 1. Tracing back: N = 7. After division by 5, remainder 1, so 7 = 5c + 1 gives c = 1. After division by 2, remainder 1, so 7 = 2d + 1 gives d = 3. The least number satisfying all conditions is 73.

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