Exam Scores

Algebra Level 2

Ten students sit for an exam which has the maximum score of 100. The average of the 10 scores was 92. What are the minimum
marks a student could have scored?


The answer is 20.

Lim Xiangying by Lim Xiangying , 21, Singapore

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2 solutions

Steve Gualtieri
Jan 30, 2018

Let s i s_i be the score of the i i -th student, with i i ranging from 1 1 to 10 10 .

The average score is 1 10 ∑ i = 1 10 s i = 92 \frac{1}{10}\sum^{10}_{i=1}s_i=92 , hence the sum of the 10 votes is 920 920 . If 9 out of 10 students achieved a score of 100, then the 10-th would have gotten a score of 20 20 .

Since nobody can score more than 100, then 20 is the lowest possible score.

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Lim Xiangying
Dec 29, 2017

(20+9x100=920 divided by 10=92)

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