ACT · Math · Integrating Essential Skills

Percentages

Percentages is part of Integrating Essential Skills in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include percent of a quantity, percent increase or decrease, successive percent changes and find the original value.

Common traps: treating 15 percent as 1.5; dividing instead of multiplying; taking the percent of the wrong quantity.

Sample questions

Question 1
From last year to this year, the number of volunteers at a food bank decreased from 200 to 170. By what percent did it change?
- A.
  85%
- B.
  30%
- C.
  17.6%
- D.
  15%
Answer: D. 15%
Percent change = |new - old|/old × 100 = 30/200 × 100 = 15%.
Question 2
During a festival week, the price of a pair of headphones at an online store in Mumbai rose by 25% to 1,440 rupees. What was the price before the increase, in rupees?
- A.
  1,080
- B.
  1,152
- C.
  1,800
- D.
  5,760
Answer: B. 1,152
The new price is 125% of the old: 1.25 × P = 1,440, so P = 1,152 rupees. Choice A (1,080) takes 25% off the new price. Choice C (1,800) adds 25% to the new price. Choice D (5,760) divides the new price by 0.25.
Question 3
A delivery drone in Singapore flies 45 minutes on a full battery when empty. Carrying a package makes it use 25% more power each minute. How many minutes can it fly with the package?
- A.
  11.25
- B.
  33.75
- C.
  36
- D.
  56.25
Answer: C. 36
Using 1.25 times the power per minute makes the battery last 1/1.25 as long: 45 ÷ 1.25 = 36 minutes. Choice A (11.25) finds 25% of 45. Choice B (33.75) takes 25% off the time, 0.75 × 45. Choice D (56.25) adds 25% to the time instead of dividing by 1.25.
Question 4
A stadium ticket has a list price of 60 dollars. A member discount of 25% is taken first, then a 20% coupon is taken off the reduced price, and finally a 5% service fee is added to what remains. What is the final price?
- A.
  34.65
- B.
  36.00
- C.
  37.80
- D.
  56.70
Answer: C. 37.80
After the member discount: 60 × 0.75 = 45. After the coupon: 45 × 0.8 = 36. With the fee: 36 × 1.05 = 37.80 dollars. Choice A (34.65) adds the two discounts; Choice B (36.00) leaves out the service fee; Choice D (56.70) treats the coupon as an increase.
Question 5
A group ticket order for a school play in Nairobi received a 20% group discount on the list total, and then 16% tax was added to the discounted amount. The final bill was 55,680 shillings. What was the list total before the discount?
- A.
  48,000
- B.
  60,000
- C.
  64,589
- D.
  69,600
Answer: B. 60,000
Undo the tax: 55,680 ÷ 1.16 = 48,000. Undo the discount: 48,000 ÷ 0.8 = 60,000 shillings. A undoes only the tax. C applies another 16% instead of undoing it. D undoes only the discount, leaving the tax in the total.

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