A student on her first 3 tests receives on an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests?

Explanation:

1. Initial average: For the first 3 tests, the average score is N. This means the total score for the first 3 tests is 3 * N.

2. Fourth test score: The student exceeds her previous average score (N) by 20 points. So, the score on the fourth test is N + 20.

3. Total score for 4 tests: Add the total score from the first 3 tests and the score from the fourth test. Total score = (3 * N) + (N + 20) = 3N + N + 20 = 4N + 20.

4. Average score for 4 tests: Divide the total score for 4 tests by 4. Average = (4N + 20) / 4 = (4N / 4) + (20 / 4) = N + 5.

Therefore, the average score for the first 4 tests is N + 5.

Analysis of Options: A) N + 20: This would be the average if the total score for 4 tests was 4N + 80, which is incorrect. It's the score of the fourth test, not the new average. B) N + 10: This would be the average if the total score for 4 tests was 4N + 40, which is incorrect. C) N + 4: This would be the average if the total score for 4 tests was 4N + 16, which is incorrect. D) N + 5: This is the correct average as calculated above. The 20 extra points from the fourth test are distributed among 4 tests, so each test's average effectively increases by 20/4 = 5 points.