Multiple Choice Question (MCQ)

When the positive integer m is divided by 7, the remainder is 4. What is the remainder when 2m is divided by 7 ?

  1. ×

    0

  2. 1

  3. ×

    4

  4. ×

    6

  5. ×

    8

Collected in the board: Number Theory

Steven Zheng posted 16 hours ago

Answer

  1. If m is divided by 7, the remainder is 4

    m = 7q+4 (q is positive integer)

    Then

    2m = 2(7q+4) = 14q+8

    When divided by 7,

    \dfrac{2m}{7} = \dfrac{14q+8}{7} = 2q+1+\dfrac{1}{7}

    Therefore the remainder is 1

    For example, 11 is divided by 7, the remainder is 4. When 22 is divided by 7, the remainder is 1.

    B is correct

Steven Zheng posted 16 hours ago

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