Question

    Find the largest four-digit number which when divided

    by 7, 13, 14, and 20, leaves a remainder 1, 7, 8, and 14 respectively.
    A 9,094 Correct Answer Incorrect Answer
    B 9,101 Correct Answer Incorrect Answer
    C 9,086 Correct Answer Incorrect Answer
    D 9,080 Correct Answer Incorrect Answer

    Solution

    Here we can see that the difference (6) between numbers and remainder is same along all four numbers. 7 = 7¹
    13 = 13¹
    14 = 2 × 7
    20 = 2² × 5 LCM of (7, 13, 14, 20) = 2² × 5 × 7 × 13
    = 4 × 5 × 7 × 13
    = 1820 Largest four-digit number which is a multiple of 1820 = 9,100 So, the required number = 9100 − 6 = 9,094

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