Five consecutive even numbers in set x sum to 440. What is the sum of five consecutive integers whose second smallest element is 121 less than twice the smallest element of set x?
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Answer: B. 240
Explanation
Five consecutive even numbers summing to four forty have a middle value of eighty eight. The smallest element of set x is eighty four, leading to a new second smallest element of forty eight. Summing the resulting five consecutive integers based on the new starting point yields a total of two forty. Consecutive even numbers differ by exactly two units across the sequence progression. The average of an odd count of consecutive numbers always equals the exact middle element. Consecutive integers increase by exactly one unit successively from the starting element.
Number theory puzzles frequently test manipulation of sequences defined by arithmetic progressions. Computer algorithms generate sequences of even and odd numbers for encryption and testing routines. Statistical resampling methods often analyze consecutive subsets of numerical data distributions. Option a results from an arithmetic miscalculation during the summation of the new integer set. Option c overestimates the sequence sum by incorrectly evaluating the starting element offset. Option d fails to match the exact sum of the consecutive integers derived from the formula.
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- Mathematics
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- Mathematics
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