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    Question

    Find the smallest number which when divided by 7, 9 and

    12 leaves a remainder 5 in each case.
    A 257 Correct Answer Incorrect Answer
    B 239 Correct Answer Incorrect Answer
    C 247 Correct Answer Incorrect Answer
    D 263 Correct Answer Incorrect Answer

    Solution

    Let the number be N. N тЙб 5 (mod 7), (mod 9), (mod 12) тЗТ N тИТ 5 is divisible by 7, 9 and 12 LCM(7, 9, 12): 7 = 7 9 = 3┬▓ 12 = 2┬▓ ├Ч 3 LCM = 2┬▓ ├Ч 3┬▓ ├Ч 7 = 4 ├Ч 9 ├Ч 7 = 252 So N тИТ 5 = 252 тЗТ N = 252 + 5 = 257

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