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      Question

      The average score obtained by 29 students in a class

      test is 68 marks. The top place was shared by 3 people who got the same score. If the lowest score was 40 marks, then which of the following could be the highest score obtained by toppers? (Marks scored by each student is a whole number)
      A 300 Correct Answer Incorrect Answer
      B 312 Correct Answer Incorrect Answer
      C 315 Correct Answer Incorrect Answer
      D 310 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      To maximize the toppers score, we must minimize the scores of everyone else. So, let the scores of other 26 students be 40 marks each. So, total marks obtained by 26 students = 40 x 26 = 1040 Remaining marks = 1972 - 1040 = 932 So, score of toppers = 932 ÷ 3 = 310 marks +  2 additional mark This additional mark could be obtained by any other student.

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