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Ques)The average (arithmetic mean) of 16 students first quiz

Expert replies
by alanforde800Maximus » Sun Sep 18, 2016 1:45 am
Ques)The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student
dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?
a) 10
b) 25
c) 40
d) 55
e) 70

Please assist with above problem.
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Source: — Problem Solving |

by GMATGuruNY » Sun Sep 18, 2016 3:20 am
alanforde800Maximus wrote:Ques)The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student
dropped the class, the average of the remaining scores increased to 64.0. What is the quiz score of the student who dropped the class?
a) 10
b) 25
c) 40
d) 55
e) 70
Total for all 16 students = (number of students)(average per student) = (16)(62.5) = 1000.
After one student drops the class, the total for the remaining 15 students = (number of students)(average per student) = (15)(64) = 960.
Score for the student who dropped the class = (total for all 16 students) - (total for the remaining 15 students) = 1000-960 = 40.

The correct answer is C.
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by [email protected] » Sun Sep 18, 2016 11:37 am
Hi alanforde800Maximus,

This question is a 'weighted average' question that gives you all of the numbers to work with, so solving it with arithmetic (the way that Mitch did) is a pretty standard approach for this type of prompt. There's a built-in concept that you can take advantage of to save some time though.

The one score that was removed from the total was small enough that it raised the average of the remaining 15 scores from a 62.5 to a 64. That 1.5 point increase per person, in total, would be (1.5)(15) = 22.5 points.

So the removed score had to be 22.5 points lower than the original average: 62.5 - 22.5 = 40.

Final Answer: C

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by MBA Challengers » Mon Sep 19, 2016 8:52 am
Avg of 16 student scores = 62.5
Total scores of the 16 students = 62.5 x 16 = 1000
Avg of 15 student scores = 64
Total scores of the 15 students = 64 x 15 = 960
Score of the 16th student = (Total of 16 student scores) - (Total of 15 student scores)
= 1000 - 960
= 40

Hence, the answer is Option C.
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