ACT Math Quiz: Percents

What this quiz covers

This quiz focuses on Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for ACT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $15
2. $35 (correct answer)
3. $20
4. $30

Explanation: This question asks for the sale price after a 30% discount on a $50 shirt. First find the discount amount: 30% of $50 = 0.30 × $50 = $15. Then subtract from the original price: $50 - $15 = $35. Choice A ($15) incorrectly gives just the discount amount rather than the final sale price.

Question 2

1. 27 (correct answer)
2. 30
3. 20
4. 18

Explanation: This question asks us to find 30% of 90. To find a percent of a number, convert the percent to a decimal and multiply: $30\% = 0.30$. Calculate: $0.30 \times 90 = 27$. Choice B (30) represents the error of confusing the percent value with the result.

Question 3

1. $\frac{75}{100}$
2. $\frac{3}{4}$ (correct answer)
3. $\frac{4}{3}$
4. $\frac{7}{5}$

Explanation: We need to convert 75% to a fraction in simplest form. First write 75% as 75/100, then simplify by finding the greatest common factor: 75/100 = (75÷25)/(100÷25) = 3/4. Choice A (75/100) is not in simplest form, and choices C and D represent values greater than 1.

Question 4

1. 20%
2. 30% (correct answer)
3. 25%
4. 15%

Explanation: This question asks for the discount percentage when a $40 shirt is sold for $28. Percent decrease is $(original - sale price) \div original \times 100$. Here:$(40 - 28) \div 40 \times 100 = 12 \div 40 \times 100 = 0.30 \times 100 = 30%$. Choice C incorrectly calculated 25%, possibly using the wrong denominator or making an arithmetic error.

Question 5

1. $25\%$
2. $75\%$ (correct answer)
3. $133\frac{1}{3}\%$
4. $30\%$

Explanation: We need to find what percent 30 correct answers is out of 40 total questions. To find what percent one number is of another, use (part/whole) × 100. Here: (30/40) × 100 = 0.75 × 100 = 75%. Choice A (25%) incorrectly uses the difference (10/40) instead of the part over the whole.

Question 6

1. $52 (correct answer)
2. $45
3. $78
4. $13

Explanation: We need to find the discounted price of a $65 sweater with a 20% discount. First find the discount amount: 20% of $65 = 0.20 × $65 = $13. Then subtract from the original price: $65 - $13 = $52. Choice D ($13) is just the discount amount, not the final price.

Question 7

1. 120 (correct answer)
2. 144
3. 300
4. 480

Explanation: This is a two-step percentage question. Choice A (120) is correct — first find the base number: 1.20 × x = 360 → x = 300. Then find 40%: 0.40 × 300 = 120. Choice B (144) skips finding the base number and takes 40% of 360 directly: 0.40 × 360 = 144. This confuses the given quantity (360) with the base number (300). Choice C (300) correctly finds the base number but stops there — reporting the intermediate result instead of answering the actual question, which asks for 40% of that number. Choice D (480) applies the wrong percentage, possibly computing 160% of 300 = 480. Pro tip: Multi-step percent problems require full execution. Read the question carefully at the end — here it asks for 40% of the original number, not for the original number itself. Finding 300 is the setup, not the finish.

Question 8

1. $80.00
2. $96.00
3. $100.00 (correct answer)
4. $120.00

Explanation: This is a multi-step percentage question testing sequential operations. Choice C ($100.00) is correct — let P = original price. After 20% discount: P × 0.80. After 10% tax on the discounted price: P × 0.80 × 1.10 = P × 0.88. Set equal to $88: P × 0.88 = 88 → P = $100. Choice A ($80.00) undoes only the tax but not the discount: $88 ÷ 1.10 = $80 — finding the pre-tax discounted price rather than the original price. Choice B ($96.00) undoes only the discount but not the tax: $88 ÷ 0.80 = $110... wait — that gives $110. $96 may come from $88 + 10$120.00) applies a single combined reversal incorrectly, possibly computing $88 ÷ 0.80 + tax error. Pro tip: Work backwards through sequential percentage changes. The final price $88 = original × 0.80 × 1.10. To find the original, divide by BOTH factors: $88 ÷ (0.80 × 1.10) = $88 ÷ 0.88 = $100. Never undo just one of the percentage operations.

Question 9

1. 80
2. 90
3. 100 (correct answer)
4. 120

Explanation: The correct answer is C (100). First find the original number: if 30% of x = 60, then x = 60 ÷ 0.30 = 200. Then find 50% of that number: 0.50 × 200 = 100. A (80) likely comes from an unclear arithmetic path, possibly computing 60 + 20. B (90) results from estimating or making an error when computing the ratio 50/30 × 60. D (120) is the most common trap — doubling the given value (60 × 2 = 120) instead of first finding the base number. The key insight is that you must find the whole (200) before computing the new percentage.

Question 10

1. 55
2. 50
3. 40
4. 45 (correct answer)

Explanation: This question asks us to find 60% of 75. To find a percent of a number, convert the percent to a decimal and multiply: $60\% = 0.60$. Calculate: $0.60 \times 75 = 45$. Choice B (50) might result from incorrectly calculating 2/3 of 75 or making an arithmetic error.

Question 11

1. $3$
2. $30$ (correct answer)
3. $3000$
4. $15$

Explanation: We need to find $15\%$ of 200. To find a percent of a number, convert the percent to a decimal and multiply: $15\% = 0.15$, so $0.15 \times 200 = 30$. Choice A ($3$) incorrectly omits a zero, and choice C ($3000$) incorrectly multiplies by 15 instead of 0.15.

Question 12

1. 45 (correct answer)
2. 40
3. 50
4. 55

Explanation: This question asks for 50% of 90. To find a percent of a number, convert the percent to a decimal and multiply. $50\% = 0.50$, so $0.50 \times 90 = 45$. Choice B incorrectly calculated approximately 44% of 90, while choice C used 55% instead of 50%.

Question 13

1. 15%
2. 20%
3. 25% (correct answer)
4. 30%

Explanation: This question asks what percent 125 is of 500. To find what percent one number is of another, use (part ÷ whole) × 100. Here: (125 ÷ 500) × 100 = 0.25 × 100 = 25%. Choice B incorrectly calculated 20%, while choice A gave 15%, both showing computational errors in the division.

Question 14

1. $\frac{1}{4}$ (correct answer)
2. $\frac{1}{2}$
3. $\frac{1}{3}$
4. $\frac{2}{5}$

Explanation: This question asks to convert the decimal 0.25 to a fraction. $0.25 = \frac{25}{100}$, which simplifies by dividing both numerator and denominator by 25: $25 \div 25 = 1$ and $100 \div 25 = 4$, giving $\frac{1}{4}$. Choice B incorrectly gives $\frac{1}{2}$, which equals $0.50$, not $0.25$.

Question 15

1. $63$
2. $3$
3. $270$
4. $27$ (correct answer)

Explanation: We need to find 30% of 90. To find a percent of a number, convert the percent to a decimal and multiply: 30% = 0.30, so 0.30 × 90 = 27. Choice B (3) incorrectly divides by 30 instead of multiplying by 0.30, and choice C (270) incorrectly multiplies by 30 instead of 0.30.

Question 16

1. $4\%$
2. $25\%$ (correct answer)
3. $60\%$
4. $400\%$

Explanation: We need to find what percent 20 is of 80. To find what percent one number is of another, use (part/whole) × 100. Here: (20/80) × 100 = 0.25 × 100 = 25%. Choice A (4%) incorrectly uses 20/500, and choice C (60%) incorrectly calculates 80-20 as a percent.

Question 17

1. 25%
2. 15%
3. 20% (correct answer)
4. 30%

Explanation: This question asks for the percent decrease from 150 to 120. Percent change is (new value - original value)/original value × 100. Calculate: (120 - 150)/150 × 100 = -30/150 × 100 = -0.20 × 100 = -20%, so the decrease is 20%. Choice B (15%) might result from using 120 as the denominator instead of 150.

Question 18

1. $100 (correct answer)
2. $90
3. $95
4. $85

Explanation: This question asks for the new price of an $80 item marked up by 25%. Calculate the markup: 25% of $80 = 0.25 × $80 = $20. Add to the original price: $80 + $20 = $100. Choice C ($95) might result from calculating an 18.75% markup instead of 25%.

Question 19

1. $20\%$
2. $25\%$ (correct answer)
3. $3\%$
4. $80\%$

Explanation: This problem asks for the percent increase from 12,000 to 15,000 people. Percent change is calculated as (new value - original value)/original value × 100. Here, (15,000 - 12,000)/12,000 × 100 = 3,000/12,000 × 100 = 0.25 × 100 = 25%. Choice A (20%) might result from incorrectly using the new value as the denominator instead of the original value.

Question 20

1. 20% (correct answer)
2. 25%
3. 30%
4. 15%

Explanation: This question asks for the percent decrease from 250 to 200. Percent change is (new value - original value)/original value × 100. Calculate: (200 - 250)/250 × 100 = -50/250 × 100 = -0.20 × 100 = -20%, so the decrease is 20%. Choice B (25%) might result from using 200 as the denominator instead of 250.