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    Question

    How many values can 'x' take if the number 7531xk must be

    divisible by 15 for any valid digit 'k'?
    A 12 Correct Answer Incorrect Answer
    B 10 Correct Answer Incorrect Answer
    C 5 Correct Answer Incorrect Answer
    D 7 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Divisible by 15 ⇒ divisible by both 5 and 3

    Divisible by 5: last digit k must be 0 or 5

    Divisible by 3: sum of digits must be divisible by 3

    Case 1: k = 0

    Sum = 7 + 5 + 3 + 1 + x + 0 = x + 16

    Divisible by 3 ⇒ x = 2, 5, 8

    Case 2: k = 5

    Sum = 7 + 5 + 3 + 1 + x + 5 = x + 21

    Divisible by 3 ⇒ x = 0, 3, 6, 9

    Total values of x: 3 (case 1) + 4 (case 2) = 7 values

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