NMOS 2010 Q20

Q20 Twenty students took a test worth 100 marks. All their results were positive integers and none of them had the same score. Their teacher ranked them from the highest score (1st) to the lowest score (20th). The top 10 students had an average of 92 marks and the next 10 students have an average of 80 marks. The top 5 students had an average that was 12 marks higher than average of the next 15 students. Find the lowest possible score of the student in the 20th rank.


92 --> 91, 90, 89, 88, 87 (lowest)


           93, 94, 95, 96, 97

 80 --> 86, 85, 84, 83, 82, 81, 80, 79, 78, ? (lowest)

86 + 85 + 84 + 83 + 82 + 81 + 80 + 79 + 78 = 738

80 x 10 = 800

800 - 738 = 62 (lowest)


93 + 94 + 95 + 96 + 97 = 475


475 / 5 = 95


91 + 90 + 89 + 88 + 87 = 445


800 + 445 = 1245


1245 / 15 = 83




95 – 83 = 12 (as given in question)

So lowest possible score is 62.