PARCC Percent and Ratio Practice Questions 1 — Questions and Answers
Question 1: 1. Rick renovated his home. He made his bedroom 40% larger (length and width) than its original size. If the original dimensions were 144 inches by 168 inches, how big is his room now if measured in feet?
- 12 ft x 14 ft
- 16.8 ft x 19.6 ft (Correct answer)
- 4.8 ft x 5.6 ft
- 201.6 ft x 235.2 ft
Correct answer: 16.8 ft x 19.6 ft
First, convert the original dimensions from inches to feet by dividing by 12: 144 inches = 12 ft and 168 inches = 14 ft. Next, increase each dimension by 40%, which means multiplying by 1.40 (100% + 40%). The new length is 12 ft * 1.40 = 16.8 ft, and the new width is 14 ft * 1.40 = 19.6 ft.
Question 2: 2. Maria paid $28.00 for a jacket that was discounted by 30%. What was the original price of the jacket?
- $36.00
- $47.60
- $40.00 (Correct answer)
- $42.50
Correct answer: $40.00
If the jacket was discounted by 30%, Maria paid 100% - 30% = 70% of the original price. So, the $28 she paid represents 70% (or 0.70) of the original price. To find the original price, divide the amount paid by the percentage paid: $28 / 0.70 = $40.00.
Question 3: 3. Derek received 6 job offers from the 15 interviews he did last month. Which ratio best describes the relationship between the number of jobs he was not offered and the number of jobs for which he interviewed?
- 6/15
- 15/6
- 3/5 (Correct answer)
- 2/3
Correct answer: 3/5
Derek received 6 job offers out of 15 interviews, meaning he was not offered 15 - 6 = 9 jobs. The question asks for the ratio of jobs he was not offered to the total number of jobs for which he interviewed, which is 9/15. This fraction simplifies to 3/5 by dividing both the numerator and denominator by their greatest common divisor, 3.
Question 4: 4. Gordon purchased a television when his local electronics store had a sale. The television was offered at 30% off its original price of $472. What was the sale price that Gordon paid?
- $141.60
- $225.70
- $305.30
- $330.40 (Correct answer)
Correct answer: $330.40
If the television was offered at 30% off its original price of $472, you first calculate the discount amount: $472 * 0.30 = $141.60. Then, subtract the discount from the original price to find the sale price: $472 - $141.60 = $330.40. Alternatively, Gordon paid 100% - 30% = 70% of the original price, so $472 * 0.70 = $330.40.
Question 5: 5. Within a certain nursing program, 25% of the class wanted to work with infants, 60% of the class wanted to work with the elderly, 10% of the class wanted to assist general practitioners in private practices, and the rest were undecided. What fraction of the class wanted to work with the elderly?
- 1/4
- 1/10
- 3/5 (Correct answer)
- 1/20
Correct answer: 3/5
The question specifically asks for the fraction of the class that wanted to work with the elderly. The problem states that 60% of the class wanted to work with the elderly. To convert a percentage to a fraction, divide the percentage by 100 (60/100) and then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, 20, resulting in 3/5.
Question 6: 6. Veronica has to create the holiday schedule for the neonatal unit at her hospital. She knows that 35% of the staff members will not be available because they are taking vacation days during the holiday. Of the remaining staff members who will be available, only 20% are certified to work in the neonatal unit. What percentage of the TOTAL staff is certified and available to work in the neonatal unit during the holiday?
- 7%
- 13% (Correct answer)
- 65%
- 80%
Correct answer: 13%
If 35% of staff are on vacation, then 100% - 35% = 65% of the staff are available. Of these available staff members, 20% are certified for the neonatal unit. To find the percentage of the total staff that is both certified and available, multiply these two percentages: 0.65 * 0.20 = 0.13, which is 13%.
Question 7: 7. A patient requires a 30% decrease in the dosage of his medication. His current dosage is 340 mg. What will his dosage be after the decrease?
- 70
- 238 (Correct answer)
- 270
- 340
Correct answer: 238
To find the new dosage, first calculate the amount of the decrease: 30% of 340 mg is 0.30 * 340 mg = 102 mg. Then, subtract this decrease from the current dosage: 340 mg - 102 mg = 238 mg. Alternatively, a 30% decrease means the new dosage is 70% of the original, so 0.70 * 340 mg = 238 mg.
Question 8: 8. A study about anorexia was conducted on 100 patients. Within that patient population 70% were women, and 10% of the men were overweight as children. How many male patients in the study were NOT overweight as children?
- 3
- 10
- 27 (Correct answer)
- 30
Correct answer: 27
In a study of 100 patients, if 70% were women, then 100% - 70% = 30% were men, meaning there were 30 male patients. Of these 30 male patients, 10% were overweight as children, which is 0.10 * 30 = 3 male patients. Therefore, the number of male patients who were NOT overweight as children is 30 - 3 = 27.
Question 9: 9. Susan is extremely excited about starting her first job as a nurse. Her gross annual salary is $40,000. Susan contributes 10% of her salary before taxes to a retirement account. Then she pays 25% of her remaining salary in state and federal taxes. Finally, she pays $30 per month for health insurance. What is Susan's annual take-home pay?
- $25640
- $25970
- $26640 (Correct answer)
- $26970
Correct answer: $26640
First, calculate Susan's retirement contribution: 10% of $40,000 = $4,000. Her remaining salary before taxes is $40,000 - $4,000 = $36,000. Next, calculate taxes: 25% of $36,000 = $9,000, leaving $36,000 - $9,000 = $27,000 after taxes. Finally, subtract annual health insurance costs: $30/month * 12 months = $360. Susan's annual take-home pay is $27,000 - $360 = $26,640.
Question 10: 10. In order for a school to allow a vending machine to be placed next to the cafeteria, 65% of the school's population must ask for it. If 340 of the school's 650 students have requested the vending machines, how many more are needed to get the vending machines?
- 75
- 83 (Correct answer)
- 89
- 99
Correct answer: 83
To get the vending machines, 65% of the 650 students are needed. This means 0.65 * 650 = 422.5 students. Since you can't have half a student, at least 423 students must request it. As 340 students have already requested, an additional 423 - 340 = 83 students are needed.
PARCC Percent and Ratio Practice Questions 1
1.
Rick renovated his home.
He made his bedroom 40% larger (length and width) than its original size.
If the original dimensions were 144 inches by 168 inches, how big is his room now if measured in feet?
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