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The average score of three-fourths of the class is 80% of the class average. Find the ratio of the average score of the remaining students to that of the entire class.

1. 3:7
2. 8:5
3. 4:9
4. 9:4

Correct answer: 8:5

Solution

Let the class average be 100. Then the average of three-fourths of the class is 80, so the total score of that group is $\frac{3}{4}n \times 80$. Using the overall average, the remaining one-fourth must have average 160, giving the ratio 160:100 = 8:5.

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