Multiple choice

The average (arithmetic mean) test score for all the students in a class is 79.6. If the average score of 16 boys in the class was 81, while that of n girls was 78, what is the value of n?

  1. 14

  2. 15

  3. 16

  4. 17

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A Correct answer
Explanation

Total score = 79.6 * (16 + n). Boys' total = 16 * 81 = 1296. Girls' total = n * 78. 1296 + 78n = 79.6 * (16 + n). 1296 + 78n = 1273.6 + 79.6n. 22.4 = 1.6n. n = 14.

AI explanation

By the method of alligation, the ratio of the number of boys to the number of girls is the difference between the girls' average and the overall average compared to the difference between the overall average and the boys' average. This gives a ratio of (79.6 minus 78) to (81 minus 79.6), which simplifies to 1.6 to 1.4, or 8 to 7. Since there are 16 boys, represented by 8 parts in the ratio, the value of n representing the girls is 7 multiplied by 2, which equals 14.