ACT Math: Integrating Essential Skills (Drill 3)

Question 1. The table below shows the monthly electricity bills for a household over four months.

Month           Bill
January       $145
February      $132
March         $118
April          $97

What is the average monthly electricity bill over these four months?

• A) $118
• B) $123 ✓
• C) $125
• D) $492

Explanation: Sum = $145 + $132 + $118 + $97 = $492. Average = $492 ÷ 4 = $123. Choice A is the March bill, the middle value in the sorted list, which is the median of the four values, not the mean. Choice C results from an arithmetic error in the sum: computing 145 + 132 + 118 + 97 = 500 rather than 492, then 500 ÷ 4 = $125. Choice D is the total sum ($492) rather than the average, forgetting to divide by 4.

Question 2. Printer A can print a 500-page document in 20 minutes. Printer B can print the same document in 30 minutes. If both printers work together, how many minutes will it take to print the document?

• A) 10
• B) 12 ✓
• C) 25
• D) 50

Explanation: Printer A's rate = 1/20 job per minute. Printer B's rate = 1/30 job per minute. Combined rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 job per minute. Time = 1 ÷ (1/12) = 12 minutes. Choice A results from averaging the two times: (20 + 30) ÷ 2 = 25... that gives 25, not 10. Choice A (10) results from subtracting: 30 − 20 = 10, or from computing 20 × 30 ÷ (20 + 30 + 20) = 600/50 = 12... actually 600/60 = 10. Hmm: 20 × 30 ÷ (20 + 30) = 600/50 = 12 is correct. Choice A (10) results from computing 20 ÷ 2 = 10, halving Printer A's time. Choice C results from averaging the two times: (20 + 30) ÷ 2 = 25. Choice D results from adding the two times together: 20 + 30 = 50.

Question 3. A rectangular garden measures 8 meters by 12 meters. A gardener wants to build a fence around the entire perimeter and also divide the garden into two equal halves with a fence running parallel to the shorter side. What is the total length of fencing needed?

• A) 40 meters
• B) 48 meters ✓
• C) 52 meters
• D) 56 meters

Explanation: Perimeter of the rectangle = 2(8 + 12) = 40 meters. The dividing fence runs parallel to the shorter side (8 meters), so it has length 8 meters. Total fencing = 40 + 8 = 48 meters. Choice A is the perimeter only, ignoring the interior dividing fence. Choice C results from adding a dividing fence of length 12 (the longer side) instead of 8: 40 + 12 = 52. Choice D results from adding two interior dividing fences: 40 + 8 + 8 = 56.

Question 4. A plumber charges a flat fee of $65 for a service call plus $55 per hour of labor. A customer's total bill was $230. For how many hours did the plumber work?

• A) 2.5
• B) 3 ✓
• C) 4
• D) 3.5

Explanation: Set up the equation: 65 + 55h = 230. Subtract 65: 55h = 165. Divide: h = 165 ÷ 55 = 3 hours. Choice A results from dividing the total bill by the hourly rate without subtracting the flat fee: 230 ÷ 55 ≈ 4.18... rounded to 2.5, or from computing (230 − 65) ÷ 66 = 165 ÷ 66 = 2.5 using the wrong hourly rate. Choice C results from dividing the total bill by the hourly rate: 230 ÷ 55 ≈ 4.18 ≈ 4, ignoring the flat fee entirely. Choice D results from computing (230 − 37.5) ÷ 55, subtracting half the flat fee instead of the full flat fee.

Question 5. In a school of 1,200 students, 60% participate in at least one extracurricular activity. Of those students, 35% participate in sports. How many students in the school participate in sports?

• A) 252 ✓
• B) 420
• C) 432
• D) 288

Explanation: Students in extracurriculars = 60% × 1,200 = 720. Students in sports = 35% × 720 = 0.35 × 720 = 252. Choice B results from computing only the first step and stopping: 60% × 1,200 = 720... or from computing 35% × 1,200 = 420, applying the sports percentage to all students rather than just those in extracurriculars. Choice C results from computing 60% × 1,200 = 720 and then 60% × 720 = 432, applying the 60% twice. Choice D results from computing 40% × 720 = 288, using the complement of 60% (students not in extracurriculars) as the sports percentage.