The Tests
To pass a certain test, 65 out of 100 is needed. The class average is 66. The average score of the students who pass the test is 71, and the average score of the students who fail the test is 56. It is decided to add 5 to every score, so that a few more students pass the test. Now the average score of the students who pass the test is 75, and the average score of the students who fail the test is 59. The number of students is between 15 and 30.How many students pass WITHOUT the 5 point addition?
The answer is 16.
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1 solution
Suppose the number of people passing the test=a Suppose the number of people failing the test=b Because the class average=66 then 66(a+b)=71a+56b a=2b So, the total number of students in the class=3b The total score of pass and fail in the class = 66(b+2b)=198b=71(2b)+56(b) After adding 5 to everybody's score The total number of points in the test=(66+5)(3b)=213b Suppose the number of people passing because of the 5 additional points=x so the number of people passing now=2b+x the number of people failing=b-x total points=75(2b+x)+59(b-x)=213b 150b+75x+59b-59x=209b+16x=213b b=4x 3b=12x Because x is a whole number then the total number of people(3b)= a multiple of 12. The only multiple of 12 between 15 and 30=24 so the number of people=24=3b total number of people passing before the added 5 points=2b *note that 24/3b=1 2b[24/3b]=2/3(24)=16