The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is  Answers
A) 99
B) 95
C) 98
D) 97
E) 100
The average score in an examination of 10 students of a class is 60 --&gt; the total score = 10*60= 
<gadget id="calculator">10*60</gadget>
<output>600</output>
600;   The 5 smallest scores have an average of 55 --&gt; the total score of the 5 smallest scores= 275.   From above, the total score of the 5 largest scores = 600 - 275= 
<gadget id="calculator">600 - 275</gadget>
<output>325</output>
325.   Say the 5 largest scores are a, b, c, d, and e (where a&lt;b&lt;c&lt;d&lt;e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:   a + b + c + d + e= 55 + 56 +57 + 58 + e = 325;   e = 99.   99nswer: 99.
<result>A</result>
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is