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Lê Quốc Trần Anh Coordinator

28/05/2018 at 07:23
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Pamela Wickham writes a sequence of four consecutive integers on a sheet of paper. The sum of three of these integers is 206. What is the other integer?




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    Lê Quốc Trần Anh Coordinator 02/06/2018 at 03:38

    AUTO ANSWER:

    The sum of any three consecutive integers is divisible by 3. Since 206 is not, we know it is either the sum of the first, second and fourth terms or of the first, third and fourth terms. If we call the first term in Pamela’s sequence x, then the four consecutive terms are x, x + 1, x + 2 and x + 3. Based on the two options above, we can have either x + x + 1 + x + 3 = 206 → 3x = 206 – 4 → 3x = 202 or x + x + 2 + x + 3 = 206 → 3x = 206 – 5 → 3x = 201. The latter is the only one that yields an integer value for x. Solving, we find x = 67. The other integer is x + 1 = 68. 


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