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ACT Math Help: Percents

Review real example questions for Percents in ACT Math.

Question 1 / 10

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If a $50 shirt is on sale for 30% off, what is the sale price?

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Question 1

If a $50 shirt is on sale for 30% off, what is the sale price?

$15
$35 (correct answer)
$20
$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

What is 30% of 90?

27 (correct answer)
30
20
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

Convert $75\%$ to a fraction in simplest form.

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

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

A shirt is priced at $40 and is sold for $28. What is the discount percentage?

20%
30% (correct answer)
25%
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

A test has $40$ questions, and a student answers $30$ correctly. What percent of the questions did the student answer correctly?

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

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

A sweater is discounted $20\%$ from its original price of $65. What is the discounted price?

$52 (correct answer)
$45
$78
$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

If $120\%$ of a number is 360, what is $40\%$ of that number?

120 (correct answer)
144
300
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

A retail store discounts an item by $20\\%$ during a sale. At the cash register, a $10\\%$ sales tax is applied to the discounted price.

If the final amount paid by the customer is $\\$ 88.00$, what was the original price of the item before the discount?

$80.00
$96.00
$100.00 (correct answer)
$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 $88 + 10% − 2% \= various errors. Choice D ($ 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

If $30\\%$ of a given number is $60$ , what is $50\\%$ of that same number?

80
90
100 (correct answer)
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

What is 60% of 75?

55
50
40
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.