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What is the least number which when divided by 8, 12, 18 and 24 leaves the remainders 4, 8, 14 and 20 respectively?

Correct answer: B. 68

  • A. 78
  • B. 68
  • C. 58
  • D. None

Explanation

The value 68 gives 68 ÷ 8 a remainder of 4, 68 ÷ 12 a remainder of 8, 68 ÷ 18 a remainder of 14, and 68 ÷ 24 a remainder of 20. To see it is least, the conditions modulo 8, 12 and 24 combine to n = 24k + 20, and the condition modulo 18 first allows k = 2, giving n = 68. The likely mistake is option a, which satisfies some conditions but not all of them.

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