Percents - ACT Math

1. A test has $40$ questions, and a student answers $30$ correctly. What percent of the questions did the student answer correctly?
   Answer: $75\%$ 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.
2. A store offers a 30% discount on a $120 jacket. What is the sale price?
   Answer: $84 This question asks for the sale price after a 30% discount on a $120 jacket. First, find the discount amount: 30% of $120 = 0.30 × $120 = $36. Then subtract from the original price: $120 - $36 = $84. Alternatively, the sale price is 70% of the original: 0.70 × $120 = $84. Choice C incorrectly kept the original price without applying the discount.
3. A $200 item is discounted by 15%. What is the discount amount?
   Answer: $30 This question asks for the discount amount on a $200 item with a 15% discount. To find a percent of a number, convert the percent to a decimal and multiply: 15% = 0.15. Calculate: 0.15 × $200 = $30. Choice B ($25) might result from calculating 12.5% instead of 15%.
4. Convert $75\%$ to a fraction in simplest form.
   Answer: $\frac{3}{4}$ 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.
5. A quantity increases from $150$ to $180$. What is the percent increase based on the original value?
   Answer: $20\%$ We need to find the percent increase from 150 to 180. Percent change is (new value - original value)/original value × 100. Here: (180 - 150)/150 × 100 = 30/150 × 100 = 0.2 × 100 = 20%. Choice D (30%) incorrectly uses the absolute difference as the percent without dividing by the original value.
6. What is 50% of 180?
   Answer: 90 This question asks us to find 50% of 180. To find a percent of a number, convert the percent to a decimal and multiply: $50\% = 0.50$. Calculate: $0.50 \times 180 = 90$. Choice B (80) might result from calculating 50% of 160 instead of 180, or making an arithmetic error.
7. A restaurant bill is $48 before tip. If the tip is $15\%$ of the pre-tax bill, what is the tip amount?
   Answer: $7.20 We need to find 15% of a $48 restaurant bill for the tip amount. To find a percent of a number, convert to decimal and multiply: 15% = 0.15, so 0.15 × $48 = $7.20. Choice B ($6.40) appears to use 13.33% instead of 15%, and choice D ($720) incorrectly multiplies by 15 instead of 0.15.
8. A phone costs $500 and is marked up by 10%. What is the new price?
   Answer: $550 This question asks for the new price of a $500 phone marked up by 10%. Calculate the markup: 10% of $500 = 0.10 × $500 = $50. Add to the original price: $500 + $50 = $550. Choice B ($510) might result from calculating a 2% markup instead of 10%.
9. What is 20% of 150?
   Answer: 30 This question asks for 20% of 150. To find a percent of a number, convert the percent to a decimal by dividing by 100, then multiply by the number. $20\% = 20 \div 100 = 0.20$, so $0.20 \times 150 = 30$. Choice B incorrectly calculated $20 \times 150 \div 100$ in the wrong order, while choice C mistakenly used $150 \div 2$.
10. What is the percent increase from 400 to 500?
    Answer: 25% This question asks for the percent increase from 400 to 500. Percent change is (new value - original value)/original value × 100. Calculate: (500 - 400)/400 × 100 = 100/400 × 100 = 0.25 × 100 = 25%. Choice B (20%) might result from using 500 as the denominator instead of 400.
11. What percent of 200 is 50?
    Answer: 25% This question asks what percent 50 is of 200. To find what percent one number is of another, use the formula: (part ÷ whole) × 100. Here: (50 ÷ 200) × 100 = 0.25 × 100 = 25%. Choice A incorrectly calculated 50 × 200 ÷ 100, while choice D mistakenly used 200 ÷ 50 × 100.
12. The population of a town decreased from 10,000 to 9,000. What is the percent decrease?
    Answer: 10% This question asks for the percent decrease from 10,000 to 9,000. Percent change is (new value - original value)/original value × 100. Calculate: (9,000 - 10,000)/10,000 × 100 = -1,000/10,000 × 100 = -0.10 × 100 = -10%, so the decrease is 10%. Choice B (5%) might result from using the wrong denominator in the calculation.
13. A laptop was originally priced at $1,200 and is now $900. What percent discount was applied?
    Answer: 25% This question asks for the percent discount from $1,200 to $900. Percent decrease is (original - new) ÷ original × 100. Here: (1,200 - 900) ÷ 1,200 × 100 = 300 ÷ 1,200 × 100 = 0.25 × 100 = 25%. Choice A incorrectly calculated 20%, possibly using the wrong denominator in the calculation.
14. Convert $2/5$ to a percent.
    Answer: 40% This question asks us to convert the fraction $2/5$ to a percent. First convert to a decimal: $2 ÷ 5 = 0.4$. Then convert to percent: $0.4 × 100 = 40$. Choice A (20%) might result from incorrectly calculating $1/5$ instead of $2/5$.
15. What is $12.5\%$ of $64$?
    Answer: $8$ We need to find 12.5% of 64. To find a percent of a number, convert the percent to a decimal and multiply: $12.5\% = 0.125$, so $0.125 \times 64 = 8$. Choice A ($0.8$) incorrectly uses 1.25% instead of 12.5%, and choice C ($12.5$) incorrectly uses the percent value itself instead of calculating.
16. A jacket originally costs $80 and is on sale for $25\%$ off. What is the sale price of the jacket (before tax)?
    Answer: $60 This problem asks for the sale price after applying a 25% discount to an $80 jacket. To find a sale price with a percent off, calculate the discount amount and subtract from the original price. The discount is 25% of $80, which is 0.25 × $80 = $20. Therefore, the sale price is $80 - $20 = $60. Choice A ($20) represents just the discount amount, not the final sale price.
17. A price increases from $40 to $50. What is the percent increase?
    Answer: 25% This question asks for the percent increase from $40 to $50. Percent change is (new value - original value) ÷ original value × 100. Here: (50 - 40) ÷ 40 × 100 = 10 ÷ 40 × 100 = 0.25 × 100 = 25%. Choice A incorrectly calculated 20%, possibly using the wrong denominator or making an arithmetic error.
18. A student's score increases from $64$ to $80$. What is the percent increase based on the original score?
    Answer: $25\%$ We need to find the percent increase from 64 to 80. Percent change is (new value - original value)/original value × 100. Here: (80 - 64)/64 × 100 = 16/64 × 100 = 0.25 × 100 = 25%. Choice B (20%) incorrectly uses the wrong base for calculation, and choice A (16%) gives just the difference without converting to a percent.
19. What is $15\%$ of $200$?
    Answer: $30$ 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.
20. What percent of 500 is 50?
    Answer: 10% This question asks what percent 50 is of 500. To find what percent one number is of another, use: (part/whole) × 100. Calculate: (50/500) × 100 = 0.10 × 100 = 10%. Choice A (5%) represents a common calculation error, possibly from dividing incorrectly.

Start this quiz