Multiple Choice Questions on A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves........... for CDS Exam Preparation

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Multiple Choice Questions

A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves...........

Quantitative Aptitude (CDS) Number System
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    A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a remainder 6. If the same number when divided by 11 leaves a remainder m and the resulting quotient when divided by 7 leaves a remainder n. What are the values of m and n respectively?

    1 and 4

    Correct Answer

    4 and 1

    Incorrect Answer

    3 and 6

    Incorrect Answer

    6 and 3

    Incorrect Answer
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    Explanation:

    This is an example of successive division. Let the number be N. The number and successive quotients, the successive divisors and the corresponding remainders are tabulated below:

    Quotients N q1 q2
    Divisors 7 11  
    Remainder 3 6  

    One value of N is 6(7) + 3 = 45 . In general , N = 77K + 45

    \therefore N = 11(7k + 4) + 1 i.e. m = 1 and q1 = 7k + 4, q2 = k and n = 4

    \therefore (m, n) = (1, 4 )

    By: Munesh Kumari
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