Multiple choice

Find the smallest number which when divided by 22, 24, 28, 30 and 42 leaves the remainders of 16, 18, 22, 24 and 36, respectively.

  1. 9234

  2. 9240

  3. 9324

  4. 9246

  5. 9248
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A Correct answer
Explanation

The differences between divisors and remainders are constant: 22-16=6, 24-18=6, 28-22=6, 30-24=6, 42-36=6. The number is LCM(22, 24, 28, 30, 42) - 6. LCM(22, 24, 28, 30, 42) = 9240. Number = 9240 - 6 = 9234.

AI explanation

Observe that each divisor minus its corresponding remainder equals 6, since 22 - 16 = 6, 24 - 18 = 6, 28 - 22 = 6, 30 - 24 = 6, and 42 - 36 = 6. We must find the least common multiple of 22, 24, 28, 30, and 42, which is 9240. The required smallest number is this least common multiple minus 6, giving 9240 - 6 = 9234. The result is 9234.

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