1. A: A set of six numbers with an average of 4 must have a collective sum of 24. The two numbers that average 2 will add up to 4, so the remaining numbers must add up to 20. The average of these four numbers can be calculated: 20/4 = 5.
2. A: First, calculate 12% of 56. 56 x 0.12 = 6.72 Then, add this value (the increase) to the original value of 56. 56 + 6.72 = 62.72 Rounding off, we get 62.7
3. D: Explanation: First, calculate 3% of 548 meters. 548 meters x 0.03 = 16.44 meters. Then, add it to the original height. 548 meters + 16.44 meters = 564.44 meters Rounding off, we get 564 meters.
4. A: Explanation: First, calculate 18% of 23. 23 x 0.18 = 4.14 Then, add this value (the increase) to the original value of 23. 23 + 4.14 = 27.14 Rounding off, we get 27.
5. B: The average, or arithmetic mean, is computed by totaling all the measurements and dividing by the number of measurements. Let TB represent the sum of the heights of the boys in the class, and TG the sum of the heights of the girls. If N is the number of students in the class, there are N/2 boys and N/2 girls. The average height of the boys is then . Similarly, the average height of the girls is . The average height of all the students is equal to . Therefore, , and the average height for the girls is 2 x 29 = 58.
6. C: To determine this, first determine the total distance of the round trip. This is twice the 45 miles of the one-way trip to work in the morning, or 90 miles. Then, to determine the total amount of time Elijah spent on the round trip, first convert his travel times into minutes. One hour and ten minutes equals 70 minutes, and an hour and a half equals 90 minutes. So, Elijah's total travel time was 70 + 90 = 160 minutes. Elijah's average speed can now be determined in miles per minute: miles per minute Finally, to convert this average speed to miles per hour, multiply by 60, since there are 60 minutes in an hour: Average speed (mph) = 60 x 0.5625 = 33.75 miles per hour
7. C. The total distance they will hike is 7.25 miles + 4.75 miles = 12 miles. If they hike 3 miles per hour, it will take them 4 hours to hike 12 miles.
8. B. The average rate of cooling is: hrs; = 5.33°F per hour.
9. A: Begin by determining the total cost of the onions and carrots, since these prices are given. This will equal (2 x $3.69) + (3 x $4.29) = $20.25. Next, this sum is subtracted from the total cost of the vegetables to determine the cost of the mushrooms: $24.15 - $20.25 = $3.90. Finally, the cost of the mushrooms is divided by the quantity (lbs) to determine the cost per pound: Cost per lb =
10. B: 145°F-32°F = 113°F, 113°F °4hrs = 28.25°F/ hr
