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    Question

    Which of the following pairs of non-zero values of p and q make 6-digit number 674pq0 divisible by both 3 and 11?

    A p = 5 and q = 4 Correct Answer Incorrect Answer
    B p = 2 and q = 2 Correct Answer Incorrect Answer
    C p = 5 and q = 2 Correct Answer Incorrect Answer
    D p = 4 and q = 2 Correct Answer Incorrect Answer

    Solution

    Given that 674pq0 is divisible by 3 and 11  For this question we will use divisibility rule  3 divisibility rule = sum of digits should be divisible by 3.  11 divisibility rule = sum of even places - sum of odd places = 0 ,11,22,33...... Here we have , 674pq0  According to divisibility rule of 3 => 6+7+4+p+q+0 = 17+p+q => it should be multiple of 3  So, the possible value of p+q = 1 , 4 , 7, 10, 13..... Now you can see the option or you can apply 11 rule as well. Then from the option only option 2 and 3 are satisfying the condition that sum should be 1,4,7..... but option 2 is not satisfying the divisibility rule of 11 . So option 2 can not be the answer of this question . Option 3 which is p = 5 and q =2 is satisfying both the rules of  3 and 11.   

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