What is the smallest integer which, when divided by 8, 12, 18, and 24, yields respective remainders of 4, 8, 14, and 20?
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Answer: B. 68
Explanation
The common difference between each divisor and its respective remainder is consistently four units across all cases. The least common multiple of the divisors eight, twelve, eighteen, and twenty four is calculated as seventy two. Subtracting the common difference of four from the least common multiple yields the required smallest integer of sixty eight. Remainder problems with constant divisor differences are solved by finding the least common multiple of the divisors. The least common multiple is the smallest positive integer that is divisible by all numbers in a given set. Number theory provides systematic methods for solving simultaneous congruence and remainder equations.
Seventy eight is incorrect because it exceeds the least common multiple minus four formula result. Fifty eight is too small and fails to satisfy the remainder conditions when divided by the given numbers. None of this option is incorrect because the second option provides the correct mathematical answer.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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