Question

    A three-digit number 4c7 is added

    to the number 538 to give a three-digit number 7d5 which is divisible by 9. Find the value of (d - c).
    A 2 Correct Answer Incorrect Answer
    B 4 Correct Answer Incorrect Answer
    C 7 Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    4c7 is added to 538 as shown below and the resultant number 7d5 is divisible by 9. 4 c 7 +5 3 8 7 d 5 If 7d5 is divisible by 9, then the sum of its digits should be divisible by 9. 7+d+5=12+d is divisible by 9. For 12 + d to be divisible by 9, the minimum value of d = 6. The other values are 15, 24... But since d is a single digit, these values are invalid. d = 6 and therefore d=c+2=6 c=4 d − c = 6 − 4 = 2

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