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a quiz has 25 questions with 4points awarded for each correct answer and 1 point deducted for each incorrect answer,with zero for each question omitted.John scores 77points.how many questions did he omit?

  • math -

    number correct --- x
    number incorrect --- y
    number skipped ---- 25 - x - y

    4x - y + 0(25-x-y) = 77
    4x - y = 77
    y = 4x - 77

    so 4x - 77 ≥ 0 and we also know x+y ≤ 25
    4x ≥ 77
    x ≥ 77/4 , but x must be an integer
    so x ≥20

    so we could have

    x y (s)kipped

    20 3 2
    21 7 -2 -----> invalid
    22 11 -8 ----> invalide
    etc

    the only one that will work is
    correct 20
    wrong 3
    skipped 2

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