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
A rooftop solar installation in Muscat has three arrays of panels. The number of panels in each array and the daily energy produced by each panel are shown below.
Array Panels Energy per panel per day (kWh)
North 12 4.0
South 20 5.5
East 8 4.5
What percent of the installation's total daily energy comes from the South array? (Round to the nearest tenth of a percent.)
- A.
  39.3%
- B.
  50%
- C.
  56.7%
- D.
  69.6%
Answer: C. 56.7%
Array outputs are 12 × 4.0 = 48, 20 × 5.5 = 110 and 8 × 4.5 = 36 kWh, a total of 194 kWh, and 110 ÷ 194 ≈ 56.7%. Choice A uses only the per-panel figures, 5.5 of 14.0; B uses the share of panels, 20 of 40; D leaves the East array out of the total.
Question 3
Each lap of a running track in Sharjah is the full distance around an outline made of two straight sections, each 110 m long, joined at the ends by two semicircles, each with a diameter of 60 m. A runner has completed 75% of a planned 10-lap session. To the nearest 10 meters, how far has the runner run?
- A.
  1,650
- B.
  2,100
- C.
  2,360
- D.
  3,060
Answer: D. 3,060
One lap is 2(110) + π(60) ≈ 408.5 m, and 75% of 10 laps is 7.5 laps, so the distance is about 3,064 m, or 3,060 to the nearest 10. Choice B (2,100) uses 60 instead of 60π for the curved ends; choice A (1,650) ignores the curved ends; choice C (2,360) uses 30π, half the circumference.
Question 4
After a renovation, a concert hall in Muscat has 720 seats. This is 20% fewer seats than the hall had before the renovation. How many seats did the hall have before?
- A.
  576
- B.
  740
- C.
  864
- D.
  900
Answer: D. 900
The 720 seats are 80% of the original, so the original is 720 ÷ 0.8 = 900. Choice A (576) takes 80% of 720, using the new number as the base; B (740) adds 20 seats instead of working with a percent; C (864) takes 20% more than 720.
Question 5
A salt works in Gujarat has a tank holding 500 kg of brine that is 8% salt by mass. After some water evaporates, the brine is 20% salt by mass, and no salt is lost. How many kilograms of water evaporated?
- A.
  60
- B.
  200
- C.
  300
- D.
  400
Answer: C. 300
The salt is 0.08 × 500 = 40 kg. At 20% salt the brine has mass 40 ÷ 0.20 = 200 kg, so 500 − 200 = 300 kg of water evaporated. Choice A (60) multiplies the 12-point rise in salt percent by 500; choice B (200) is the final mass of brine, not the water lost; choice D (400) takes 20% of 500 as the final mass.

Array	Panels	Energy per panel per day (kWh)
North	12	4.0
South	20	5.5
East	8	4.5

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