What is the smallest number which leaves remainders of 14, 19, 29, and 34 when divided by 20, 25, 35, and 40 respectively________?
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Answer: C. 1349
Explanation
Subtracting each remainder from its respective divisor consistently yields a uniform difference value of six. Finding the least common multiple of all the specified divisors yields a baseline value of one thousand four hundred. Subtracting the uniform difference of six from the least common multiple gives the required number thirteen forty-nine. Remainder problems with uniform differences between divisors and remainders are solved using least common multiples. The least common multiple is the smallest positive integer that is divisible by every number in a given set. Subtracting the common difference from the LCM yields the smallest number satisfying all remainder conditions.
Option A suggests nineteen ninety-four which exceeds the least common multiple calculation results significantly. Option B suggests fourteen ninety-four which fails to account for the common difference subtraction step properly. Option D suggests fourteen ninety-six which represents an incorrect arithmetic adjustment of the base LCM.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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