Multiple choice

The average of the test scores of a class of K students is 70, and the average of the test scores of a class of M students is 92. When the scores of the both classes are combined, the average score is 86. What is the value of K/M?

  1. ½

  2. 2/3

  3. 8/3

  4. 3/8

  5. 3/2
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D Correct answer
Explanation

Weighted average: (70K + 92M) / (K + M) = 86. 70K + 92M = 86K + 86M. 6M = 16K. K/M = 6/16 = 3/8.

AI explanation

Using the method of alligation, the ratio of the number of students in the two classes is inversely proportional to the differences of their averages from the combined average. The difference between the second class and the combined average is 86 minus 92, which is negative 6. The difference between the combined average and the first class is 86 minus 70, which is 16. The ratio of K to M is the absolute value of the first difference to the second difference, so K over M equals 6 over 16, which simplifies to 3/8.

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