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    Question

    Find the smallest integer greater than 100 which leaves

    remainder 4 when divided by each of 5, 6 and 7.
    A 165 Correct Answer Incorrect Answer
    B 214 Correct Answer Incorrect Answer
    C 158 Correct Answer Incorrect Answer
    D 225 Correct Answer Incorrect Answer

    Solution

    ATQ, If N leaves remainder 4 when divided by 5, 6, 7, then N тИТ 4 is divisible by all 5, 6, 7. LCM(5, 6, 7): 5 = 5 6 = 2 ├Ч 3 7 = 7 LCM = 2 ├Ч 3 ├Ч 5 ├Ч 7 = 210 So N тИТ 4 = 210k тЗТ N = 210k + 4 We want N > 100: 210k + 4 > 100 тЗТ 210k > 96 тЗТ k тЙе 1 Smallest such N is for k = 1: N = 210 ├Ч 1 + 4 = 214 Answer: 214.

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