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29 May, 02:05

When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35?

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  1. 29 May, 05:57
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    Answer: K = 4

    Step-by-step explanation: N/5 remainder is 1, N/7 remainder 3.

    Let x represent k

    Therefore, 5x + 1 = N and 7x + 3 = N

    (Where x can be 1, 2, 3, 4,5, 6 ...)

    Substitute values of x until you get similar values of N,

    Such that

    When x is 6,

    5 (6) + 1 = 31 and

    When x is 4

    7 (4) + 3 = 31.

    If K + N/35 must be equal to 1 to find the least value, the K = 4 so that 4 + 31/35 = 1.

    Therefore K = 4.
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