This presentation gives solution for CAT Level Qn 4 from the book Quantitative Aptitude for CAT. Solutions have been compiled by Rajesh Balasubramanian, director of 2IIM.
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1. Average CAT Level 2
Question No. 4 from Quantitative Aptitude for CAT
2. 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 40 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......
a) 99 b) 100
c) 87 d) 95
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3. Q. 4 from Average
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 40 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......
10 students have scored 600 marks amongst them, and no one is
allowed to score lesser than 40 or higher than 100. The idea now is
to maximize what the highest scorer gets.
4. Q. 4 from Average
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 40 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......
The 5 least scores have an average of 55, which means that they have scored
55 x 5 = 275 marks amongst them. This leaves 325 marks to be shared
amongst the top 5 students. Lets call them a, b, c, d and e. Now, in order to
maximize what the top scorer “e” gets, all the others have to get the least
possible scores (and at the same time, they should also get distinct integers.)
5. Q. 4 from Average
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 40 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......
The least possible score of the top 5 should be at least equal to the highest
of the bottom 5. Now we want to make sure that the highest of the bottom 5
is the least possible. This can be done by making all scores equal to 55. If
some scores are less than 55, some other scores have to be higher than 55
to compensate and make the average 55. Thus the highest score is the least
only when the range is 0.
6. Q. 4 from Average
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 40 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......
So now, we have the lowest value that the top 5 can score, which is
55. The others have to get distinct integer scores, and as few marks
as possible, so that “e” gets the maximum.
So, 55 + 56 + 57 + 58 + e = 325
e = 99 marks. Answer choice (a)
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