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    Question

    In an institute, the average score on an IBACIO

    Scholarship test for 52 aspirants is 51. Excluding the scores of the top 5 performers, the average score of the remaining aspirants drops by 3. None of the first five highest scores is below 60, and each of the top 5 scorers has distinct integral scores. Determine the maximum possible score of the top performer, considering the maximum score is 200.
    A 250 Correct Answer Incorrect Answer
    B 265 Correct Answer Incorrect Answer
    C 150 Correct Answer Incorrect Answer
    D 100 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the score of the topper be 'x' Total score of 52 aspirants = 52 × 51 = 2652 Total score of remaining 47 aspirants after scores of the best five performers are removed  = 47 × 48 = 2256 Total score of the top five aspirants = 2652 – 2256 = 396 x + (total score of the next 4 top scores) = 396 x is the maximum when the total score of the next 4 top scorers is minimum. Total score of the next 4 top scorers has a minimum value of 60 + 61 + 62 + 63 = 246  (since all the top 5 scores are distinct) and the least is 60. Therefore, 'x' has a maximum value of 396 – 246 = 150

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