Medium ACT Percentage Practice Questions

Mastering ACT Percentage problems is a vital step for any student aiming for a top-tier score on the math section of the ACT. Percentages appear in various forms, ranging from simple calculations to complex multi-step word problems involving discounts, taxes, and population growth. This guide provides a comprehensive overview of the strategies needed to solve medium-difficulty percentage questions effectively.

To succeed on the ACT, you must navigate the transition from basic arithmetic to algebraic applications. Understanding how to manipulate the relationship between parts, wholes, and rates is essential. For more foundational work, you might want to look at ACT Percentage Practice Questions with Answers before tackling these intermediate challenges. Using tools like an AI Question Generator can also help you simulate the variety of questions you will encounter on test day.

Concept Explanation

An ACT Percentage problem typically requires finding a part, a whole, or a percentage rate by using the fundamental formula: $\text{Part} = \text{Percent} \times \text{Whole}$. On the ACT, percentages are often presented as decimals (e.g., 25% becomes 0.25) or fractions (e.g., 25% becomes $\frac{1}{4}$) to make calculations manageable.

Key concepts included in medium-level questions are:

• Percent Change: Calculated using the formula $\frac{ \text{New Value} - \text{Old Value}}{ \text{Old Value}} \times 100$.
• Successive Percentages: Applying multiple percentage changes in a row (e.g., a 20% discount followed by a 10% tax). Note that you cannot simply add the percentages together.
• Percentage of a Percentage: Finding a portion of a subset, such as "30% of the 40% of students who play sports."

When solving these, always identify the "base" or the "whole." On the ACT, the most common trap involves using the wrong base for a calculation. For a broader look at how these fit into the exam, check out our ACT Prep hub. You can also see how these logic patterns apply to ACT Word Problems Practice Questions with Answers.

Solved Examples

Review these step-by-step solutions to understand the logic required for medium-difficulty percentage questions.

1. Example 1: Percent Increase
   A laptop originally priced at $800 is increased by 15%. After one month, the new price is decreased by 10% for a holiday sale. What is the final price of the laptop?
   1. First, find the price after the 15% increase: $800 \times 1.15 = 920$.
   2. Next, apply the 10% decrease to the new price: $920 \times 0.90 = 828$.
   3. The final price is $828.
2. Example 2: Finding the Original Whole
   After a 25% discount, a pair of shoes costs $45. What was the original price of the shoes?
   1. Let $x$ be the original price. The sale price represents 75% of the original ($100\% - 25\% = 75\%$).
   2. Set up the equation: $0.75x = 45$.
   3. Solve for $x$: $x = \frac{45}{0.75} = 60$.
   4. The original price was $60.
3. Example 3: Percent of a Percent
   In a school of 500 students, 40% are seniors. Of the seniors, 20% are in the jazz band. How many seniors are in the jazz band?
   1. Calculate the number of seniors: $500 \times 0.40 = 200$.
   2. Calculate the number of seniors in the jazz band: $200 \times 0.20 = 40$.
   3. There are 40 seniors in the jazz band.

Practice Questions

1. A jacket is on sale for 30% off the original price of $120. If a 5% sales tax is applied to the sale price, what is the final cost?
2. If 15% of a number $n$ is 45, what is 25% of $n$?
3. The population of a town increased from 12,500 to 15,000. What was the percent increase in population?

4. A rectangle's length is increased by 20% and its width is decreased by 10%. By what net percentage does the area of the rectangle change?
5. A jar contains red, blue, and green marbles. 30% are red, 50% are blue, and the remaining 12 marbles are green. How many total marbles are in the jar?
6. An investment loses 20% of its value in the first year. By what percentage must the remaining value increase in the second year to return to its original value?
7. In a group of 80 people, 60% are employed. If 25% of those employed work remotely, how many people in the group do NOT work remotely?
8. A car's value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 2 years?

Answers & Explanations

1. Answer: $88.20
   First, find the sale price: $120 \times (1 - 0.30) = 120 \times 0.70 = 84$. Next, apply the 5% tax to the sale price: $84 \times 1.05 = 88.20$.
2. Answer: 75
   Find $n$ first: $0.15n = 45 \rightarrow n = \frac{45}{0.15} = 300$. Then find 25% of 300: $0.25 \times 300 = 75$.
3. Answer: 20%
   Use the percent change formula: $\frac{15,000 - 12,500}{12,500} = \frac{2,500}{12,500} = 0.20$. Multiply by 100 to get 20%.
4. Answer: 8% Increase
   Let original length be $L$ and width be $W$. Original Area = $LW$. New Area = $(1.20L)(0.90W) = 1.08LW$. This represents a 108% of original area, or an 8% increase. This technique is also useful in ACT Geometry Practice Questions with Answers.
5. Answer: 60
   The percentage of green marbles is $100\% - (30\% + 50\%) = 20\%$. If 20% of the total $T$ is 12, then $0.20T = 12 \rightarrow T = \frac{12}{0.20} = 60$.
6. Answer: 25%
   Let the original value be 100. After a 20% loss, it is 80. To get from 80 back to 100, you need a gain of 20. The percentage increase needed is $\frac{20}{80} = 0.25$, or 25%.
7. Answer: 68
   Employed: $80 \times 0.60 = 48$. Remote workers: $48 \times 0.25 = 12$. People who do NOT work remotely: $80 - 12 = 68$.
8. Answer: $14,450
   Year 1: $20,000 \times 0.85 = 17,000$. Year 2: $17,000 \times 0.85 = 14,450$.

To further refine your skills, consider practicing with an AI Exam Simulator to get used to the timing of the ACT Math section. Understanding percentages is also a prerequisite for topics found in ACT Statistics Practice Questions with Answers and ACT Probability Practice Questions with Answers.

1. If a shirt is marked down by 40% and then an additional 10% discount is applied to the sale price, what is the total percentage discount from the original price?

• A50%
• B46%
• C44%
• D36%

Frequently Asked Questions

What is the difference between percent increase and percent decrease?

Percent increase measures how much a value has grown relative to its starting point, while percent decrease measures how much it has shrunk. Both use the difference between values divided by the original value as the base for the calculation.

Can I just add percentages together if they happen sequentially?

No, you cannot add sequential percentages because the base value changes after the first percentage is applied. For example, a 10% increase followed by a 10% decrease results in a 1% net loss, not 0% change.

How do I convert a percentage to a decimal for ACT math?

To convert a percentage to a decimal, divide the percentage by 100 or simply move the decimal point two places to the left. For instance, 7.5% becomes 0.075, which is necessary for calculation on most standard calculators used on the ACT official website.

What is the "of" rule in percentage word problems?

In math word problems, the word "of" almost always signifies multiplication. When you see "25% of 80," you should translate that into the mathematical expression $0.25 \times 80$.

How are percentages used in ACT data analysis?

Percentages are frequently used in the ACT Science and Math sections to describe data in tables and graphs. You may be asked to calculate the relative frequency or compare growth rates between two different data sets based on standard percentage definitions.