Official Guide Explanation:
Problem Solving #85




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Solution and Metadata

Question: 85
Page: 164
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: In a series of ten consecutive integers, the sixth is five greater than the first, the seventh is five greater than the second, and so on. Consider an example of the ten consecutive integers {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}. It doesn't matter what the numbers are--this is a general truth of consecutive integers. Thus, if each of the last five digits is five greater than the corresponding member of the first five digits, the difference between the sum of the first five and the last five is 5(5) = 25. If the sum of the last five digits is 25 greater than the sum of the first five, and the sum of the first five is 560, the sum of the last five is 560 + 25 = 585, choice (A).

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