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2014/15 AHSMC Part 1 Problem 6

Problem 6 of 16

The sum of four consecutive integers is nn. The largest of these four numbers is

Answer choices

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Solution

Let n=(k−3)+(k−2)+(k−1)+k=4k−6n = (k-3) + (k-2) + (k-1) + k = 4k - 6. Then k=n+64k = \dfrac{n+6}{4}. The answer is (D).