SOLUTION: Thirty-six students took a final exam on which the passing score was 70. The mean of those who passed was 78, the mean score of those who failed was 60, and the mean of all scores

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Question 549874: Thirty-six students took a final exam on which the passing score was 70. The mean of those who passed was 78, the mean score of those who failed was 60, and the mean of all scores was 71. How many students did not pass the exam?
Answer by mathstutor458(57) About Me  (Show Source):
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Total number of students are 36.
number of students who passed in the exam, let us say 'x'.
number of students who didnt passed in the exam is 36-x.
The mean of those who passed was 78
the mean score of those who failed was 60
the mean of all scores was 71.
Therefore,78x+60(36-x)=71*36
=>18x=36(71-60) => 18x=36*11 =>x=22 members paased the exam
Remaining 14 members didnt pass the exam. so, the answer is 14.