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    Question

    If a nine-digit number 89563x87y is divisible by 72,

    then the value of √ (5x -4y) will be ∶
    A 17 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C √22 Correct Answer Incorrect Answer
    D √17 Correct Answer Incorrect Answer

    Solution

    Nine-digit number 89563x87y is divisible by 72, so the number is also divisible by 8 and 9. Divisibility law of 8 ⇒ A number divisible by 8 if its last three digits are divisible by 8. Divisibility law of 9 ⇒ A number is divisible by 9 if the sum of its digits is divisible by 9. 87y divisible by 8 if y = 2 Nine-digit number 89563x872 is divisible by 9 if the sum of its digits is divisible by 9. = 8+9+5+6+3+x+8+7+2 =48+x So, putting the value of x= 6 Now -√ (5x -4y) = √ (5×6 – 4×2) = √22.

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