PARCC Estimation Sequence Practice Test 1 — Questions and Answers
Question 1: 1. If Sara can read 15 pages in 10 minutes, how long will it take her to read 45 pages?
- 20 minutes
- 30 minutes (Correct answer)
- 40 minutes
- 50 minutes
Correct answer: 30 minutes
Sara reads 15 pages in 10 minutes. To read 45 pages, which is three times the original amount (45 / 15 = 3), it will take her three times as long. Therefore, multiply her original reading time by three: 10 minutes * 3 = 30 minutes.
Question 2: 2. Restaurant customers tip their server only 8 percent for poor service. If their tip was $3.70, how much was their bill?
- $40.15
- $44.60
- $46.25 (Correct answer)
- $50.45
Correct answer: $46.25
Let 'x' represent the total bill. The tip of $3.70 represents 8% of the total bill. So, we can set up the equation: 0.08 * x = $3.70. To find 'x', divide the tip amount by the percentage (as a decimal): x = $3.70 / 0.08 = $46.25. Thus, their bill was $46.25.
Question 3: 3. Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh?
- 125 pounds
- 152 pounds (Correct answer)
- 115 pounds
- 165 pounds
Correct answer: 152 pounds
To solve this, set up two equations: E = 2B + 5 (Enrique's weight is 5 more than twice Brendan's) and E + B = 225 (their total weight). Substitute the first equation into the second to get (2B + 5) + B = 225, which simplifies to 3B + 5 = 225. Solving for Brendan's weight (B) gives 3B = 220, so B = 220/3 pounds. Then, substitute B back into the first equation to find Enrique's weight: E = 2(220/3) + 5 = 455/3 pounds, which is approximately 151.67 pounds. The closest option provided is 152 pounds.
Question 4: 4. What is the missing number in the sequence: 4, 6, 10, 18, ___, 66.
- 22
- 34 (Correct answer)
- 45
- 54
Correct answer: 34
To find the missing number, analyze the differences between consecutive terms in the sequence. The differences are 6-4=2, 10-6=4, and 18-10=8. This reveals a pattern where each difference is double the previous one. Following this pattern, the next difference should be 8 * 2 = 16. Adding this to the last known term, 18 + 16 = 34, gives the missing number. To verify, the subsequent difference would be 16 * 2 = 32, and 34 + 32 = 66, which matches the final term.
Question 5: 5. There are 64 fluid ounces in a 1\/2 gallon. If Nora fills a tank that holds 8 3\/4 gallons, how many ounces will she use?
- 560 ounces
- 1,024 ounces
- 1,088 ounces
- 1,120 ounces (Correct answer)
Correct answer: 1,120 ounces
First, determine the conversion rate for one full gallon. Since there are 64 fluid ounces in 1/2 gallon, there are 64 * 2 = 128 fluid ounces in 1 full gallon. Next, convert the tank's capacity from mixed number to decimal: 8 3/4 gallons is equal to 8.75 gallons. Finally, multiply the total gallons by the ounces per gallon: 8.75 gallons * 128 ounces/gallon = 1,120 ounces.
Question 6: 6. Shaylee goes shopping for two types of fruit: mangoes that cost $2.00 each and coconuts that cost $4.00 each. If she buys 10 pieces of fruit and spends $30.00, how many pieces of each type of fruit did she buy?
- 4 mangoes and 6 coconuts
- 5 mangoes and 5 coconuts (Correct answer)
- 6 mangoes and 4 coconuts
- 7 mangoes and 3 coconuts
Correct answer: 5 mangoes and 5 coconuts
Let 'm' be the number of mangoes and 'c' be the number of coconuts. We can set up two equations: m + c = 10 (total pieces of fruit) and 2m + 4c = 30 (total cost). From the first equation, we know m = 10 - c. Substitute this into the second equation: 2(10 - c) + 4c = 30. This simplifies to 20 - 2c + 4c = 30, or 20 + 2c = 30. Solving for 'c' gives 2c = 10, so c = 5 coconuts. Substituting c=5 back into m = 10 - c yields m = 5 mangoes.
Question 7: 7. Assuming Ed's Painting did not experience any major business changes, which of the following is likely to be closest to the number of houses he painted in 2005?
- 25
- 31 (Correct answer)
- 22
- 45
Correct answer: 31
This question requires interpreting a trend from a provided graph (not shown here). To find the likely number of houses painted in 2005, one would examine the data for previous years (e.g., 2002, 2003, 2004) to identify a pattern or trend in the number of houses painted. Based on the typical progression shown in such graphs, extrapolating the trend (e.g., a slight increase or stable number) from the preceding years would lead to an estimate of approximately 31 houses for 2005.
Question 8: 8. A house is 25 feet tall and a ladder is set up 35 feet away from the side of the house. Approximately how long is the ladder from the ground to the roof of the house?
- 43 ft (Correct answer)
- 25 ft
- 50 ft
- 62 ft
Correct answer: 43 ft
This problem forms a right-angled triangle where the house's height and the distance the ladder is from the house are the two legs, and the ladder itself is the hypotenuse. Using the Pythagorean theorem, a² + b² = c², where 'a' is 25 feet and 'b' is 35 feet. Calculate 25² + 35² = 625 + 1225 = 1850. Therefore, the length of the ladder 'c' is the square root of 1850, which is approximately 43.01 feet. The closest answer choice is 43 feet.
Question 9: 9. If Louis travels on his bike at an average rate of 20 mph, how long will it take him to travel 240 miles?
- 48 hours
- 12 hours (Correct answer)
- 20 hours
- 8 hours
Correct answer: 12 hours
To find the time it takes to travel a certain distance at a given average rate, use the formula Time = Distance / Rate. In this case, the distance is 240 miles and the average rate is 20 miles per hour. Dividing 240 miles by 20 mph gives 12 hours.
Question 10: 10. A soda company is testing a new sized can to put on the market. The new can is 6 inches in diameter and 12 inches in height. What is the volume of the can in cubic inches?
- 339 (Correct answer)
- 113
- 432
- 226
Correct answer: 339
The can is a cylinder, and its volume is calculated using the formula V = π * r² * h, where 'r' is the radius and 'h' is the height. Given the diameter is 6 inches, the radius 'r' is half of that, which is 3 inches. The height 'h' is 12 inches. Plugging these values into the formula: V = π * (3)² * 12 = π * 9 * 12 = 108π. Using the approximation π ≈ 3.14, the volume is approximately 108 * 3.14 = 339.12 cubic inches.
PARCC Estimation Sequence Practice Test 1
1.
If Sara can read 15 pages in 10 minutes, how long will it take her to read 45 pages?