PARCC Averages and Rounding Practice Questions 1 — Questions and Answers
Question 1: 1. The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?
- 5 (Correct answer)
- 6
- 7
- 8
- 9
Correct answer: 5
The sum of the six numbers is 6 * 4 = 24. The sum of two of those numbers is 2 * 2 = 4. To find the sum of the other four numbers, subtract the sum of the two from the total sum: 24 - 4 = 20. Finally, divide this sum by 4 to get their average: 20 / 4 = 5.
Question 2: 2. Kate got a 56 on her first math test. On her second math test, she raised her grade by 12%. What was her grade?
- 62.7 (Correct answer)
- 67.2
- 68.0
- 72.3
Correct answer: 62.7
To find Kate's new grade, first calculate the increase: 12% of 56 is 0.12 * 56 = 6.72. Then, add this increase to her original grade: 56 + 6.72 = 62.72. Therefore, her new grade was 62.7 when rounded to one decimal place.
Question 3: 3. A skyscraper is 548 meters high. The building's owners decide to increase its height by 3%. How high would the skyscraper be after the increase?
- 551 meters
- 555 meters
- 562 meters
- 564 meters (Correct answer)
Correct answer: 564 meters
First, calculate the increase in height by finding 3% of 548 meters: 0.03 * 548 = 16.44 meters. Then, add this increase to the original height of the skyscraper: 548 + 16.44 = 564.44 meters. Rounding to the nearest whole meter, the skyscraper would be 564 meters high.
Question 4: 4. Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
- 27 (Correct answer)
- 32
- 38
- 40
Correct answer: 27
To find the new production, calculate the 18% increase: 0.18 * 23 dolls = 4.14 dolls. Since you can't produce a fraction of a doll, round this up to 4 or consider the total as 23 * 1.18 = 27.14. Adding the increase to the original amount gives 23 + 4 = 27 dolls, or rounding 27.14 to the nearest whole doll gives 27.
Question 5: 5. A class contains an equal number of boys and girls. The average height of the boys is 62 inches. The average height of the all the students is 60 inches. What is the average height of the girls in the class?
- 57 inches
- 58 inches (Correct answer)
- 59 inches
- 60 inches
Correct answer: 58 inches
Let 'n' be the number of boys and 'n' be the number of girls. The total height of the boys is 62n. The total height of all 2n students is 2n * 60 = 120n. The total height of the girls is the total height of all students minus the total height of the boys: 120n - 62n = 58n. Since there are 'n' girls, their average height is 58n / n = 58 inches.
Question 6: 6. Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home in the evening, however, traffic was much heavier and the same trip took an hour and a half. What was his average speed in miles per hour for the round trip?
- 30
- 45
- 33 3\/4 (Correct answer)
- 32 1\/2
Correct answer: 33 3\/4
The total distance for the round trip is 45 miles * 2 = 90 miles. The total time taken is 1 hour 10 minutes + 1 hour 30 minutes = 2 hours 40 minutes, which is 2 and 40/60 hours or 2 and 2/3 hours (8/3 hours). Average speed is total distance divided by total time: 90 miles / (8/3 hours) = 90 * (3/8) = 270/8 = 33.75 mph. As a mixed number, this is 33 and 3/4 mph.
Question 7: 7. If Joey and Katrina hike an average of 3 miles per hour, about how long will it take them hike both the Beaverton Falls trail (7.25 miles) and the Copper Creek trail (4.75 miles)?
- 3 hours
- 3.5 hours
- 4 hours (Correct answer)
- 4.5 hours
Correct answer: 4 hours
First, calculate the total distance of both trails: 7.25 miles + 4.75 miles = 12 miles. Since Joey and Katrina hike at an average speed of 3 miles per hour, divide the total distance by their speed to find the total time. So, 12 miles / 3 mph = 4 hours.
Question 8: 9. Rachel spent $24.15 on vegetables. She bought 2 lbs of onions, 3 lbs of carrots, and 1 1\/2 lbs of mushrooms. If the onions cost $3.69 per lb, and the carrots cost $ 4.29 per lb, what is the price per lb of mushrooms?
- $2.60 (Correct answer)
- $2.25
- $2.80
- $3.10
- $2.75
Correct answer: $2.60
First, calculate the cost of onions (2 lbs * $3.69/lb = $7.38) and carrots (3 lbs * $4.29/lb = $12.87). The combined cost for onions and carrots is $7.38 + $12.87 = $20.25. Subtract this from the total spent ($24.15 - $20.25 = $3.90) to find the cost of the mushrooms. Finally, divide the mushroom cost by their weight to find the price per pound: $3.90 / 1.5 lbs = $2.60/lb.
Question 9: 10. A roast was cooked at 325 °F in the oven for 4 hours. The internal temperature rose from 32 °F to 145 °F. What was the average rise in temperature per hour?
- 20.2°F\/hr
- 28.25°F\/hr (Correct answer)
- 32.03°F\/hr
- 37°F\/hr
Correct answer: 28.25°F\/hr
To find the average rise in temperature per hour, first calculate the total temperature increase: 145°F - 32°F = 113°F. Then, divide this total temperature rise by the cooking time, which was 4 hours. So, 113°F / 4 hours = 28.25°F/hr.
PARCC Averages and Rounding Practice Questions 1
1.
The average of six numbers is 4.
If the average of two of those numbers is 2, what is the average of the other four numbers?