Let's denote the initial average test score of the students as $x$. According to the problem, the students increased their scores by 20 percentage points, so the post-test score can be represented as $x + 20\%$. We know that the post-test average score was 95%. Therefore, we set up the equation:

$x + 20 = 95$

Solving the equation: $x = 95 - 20 = 75$

So, the initial average test score, $x$, was 75%. This means the starting range for the grades on the test was around 75%.

Explanation:

• The problem states that the post-test score is 20% higher than the pre-test score.
• We know the post-test score is 95%, so subtracting the 20% increase from 95% gives us the initial score of 75%.

Would you like further details or have any questions?

Related Questions:

1. If the increase had been 30 percentage points instead of 20, what would the initial score be?
2. What would the post-test score be if the initial score was 70%?
3. How would the initial score change if the increase was 10 percentage points instead of 20?
4. What is the percentage increase if the initial score was 85% and the post-test score is 95%?
5. If the post-test score was 90%, what was the initial score if the increase was 15 percentage points?

Tip:

When working with percentage increases, always ensure that you correctly add or subtract the percentage from the original value to avoid mistakes.