ISEE Middle Level Quiz: Percent Problems In Context
20 questions · exam conditions
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Percent Problems In ContextQuestion 1 of 20

A fundraising event raised a total of $5,000. 30% of the money will be used for administrative costs. The remaining money will be split equally among 4 charities. How much money will each charity receive?

$875
$1,250
$3,500
$1,500
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ISEE Middle Level Quiz

ISEE Middle Level Quiz: Percent Problems In Context

Practice Percent Problems In Context in ISEE Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Percent Problems In Context, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A fundraising event raised a total of $5,000. 30% of the money will be used for administrative costs. The remaining money will be split equally among 4 charities. How much money will each charity receive?

  1. $875 (correct answer)
  2. $1,250
  3. $3,500
  4. $1,500
Explanation: First, calculate the amount of money remaining after administrative costs. If 30% is used for costs, then 70% remains for charities. The amount for charities is (0.70 \times 5,000=5,000 = 3,500). This amount is split equally among 4 charities, so each charity receives (3,500÷4=3,500 \div 4 = 875).

Question 2

A test has two sections. A student answered 80% of the 30 questions in the first section correctly. If the student scored 70% on the entire 50-question test, what percentage of the 20 questions in the second section did the student answer correctly?

  1. 55% (correct answer)
  2. 60%
  3. 65%
  4. 75%
Explanation: First, find the number of questions answered correctly in section 1: 30×0.80=2430 \times 0.80 = 24. Next, find the total number of questions answered correctly on the whole test: 50×0.70=3550 \times 0.70 = 35. The number of questions answered correctly in section 2 is the difference: 35−24=1135 - 24 = 11. Finally, find the percentage for section 2, which has 20 questions: 1120×100%=55%\frac{11}{20} \times 100\% = 55\%.

Question 3

Sarah deposits $600 into a savings account that earns 2.5% simple annual interest. If she does not make any other deposits or withdrawals, how much interest will she have earned after 3 years?

  1. $15.00
  2. $45.00 (correct answer)
  3. $645.00
  4. $4.50
Explanation: Simple interest is calculated using the formula I = Prt, where I is interest, P is principal, r is the rate, and t is time. First, find the interest for one year: (600×0.025=600 \times 0.025 = 15). Then, multiply by the number of years to find the total interest: (15×3=15 \times 3 = 45).

Question 4

In a survey, 110 students, representing 40% of the seventh-grade class, said they prefer comedy movies. How many students are in the entire seventh-grade class?

  1. 44
  2. 154
  3. 220
  4. 275 (correct answer)
Explanation: Let T be the total number of students in the class. We are given that 40% of T is 110. The equation is 0.40×T=1100.40 \times T = 110. To find T, divide 110 by 0.40: T=110÷0.40=275T = 110 \div 0.40 = 275. There are 275 students in the seventh-grade class.

Question 5

In a company, 60% of the employees are men. If 25% of the men and 50% of the women have worked at the company for more than 10 years, what percentage of all employees have worked there for more than 10 years?

  1. 35% (correct answer)
  2. 37.5%
  3. 40%
  4. 75%
Explanation: Assume there are 100 employees. Then there are 60 men and 40 women. The number of men who have worked for more than 10 years is 0.25×60=150.25 \times 60 = 15. The number of women who have worked for more than 10 years is 0.50×40=200.50 \times 40 = 20. The total number of employees who have worked for more than 10 years is 15+20=3515 + 20 = 35. Since the total number of employees is 100, this represents 35% of all employees.

Question 6

A tablet computer is priced at $400. A store offers a 15% discount. Sales tax of 8% is calculated on the discounted price. What is the total cost of the tablet?

  1. $308.00
  2. $340.00
  3. $367.20 (correct answer)
  4. $372.00
Explanation: First, calculate the discounted price. The discount is (0.15 \times 400 = 60\). The discounted price is \(400 - 60=60 = 340). Next, calculate the sales tax on this discounted price: (0.08 \times 340 = 27.20\). Finally, add the tax to the discounted price to get the total cost: \(340 + 27.20=27.20 = 367.20).

Question 7

A recipe for a smoothie requires 20 ounces of liquid. 75% of the liquid is yogurt. If the rest of the liquid is juice, how many ounces of juice are required?

  1. 5 (correct answer)
  2. 10
  3. 15
  4. 25
Explanation: If 75% of the liquid is yogurt, then the remaining percentage must be juice. The percentage of juice is 100%−75%=25%100\% - 75\% = 25\%. To find the amount of juice, calculate 25% of the total liquid volume: 0.25×20=50.25 \times 20 = 5 ounces.

Question 8

A club has 15 members who are in 7th grade and 10 members who are in 8th grade. What percentage of the club members are in 7th grade?

  1. 15%
  2. 40%
  3. 60% (correct answer)
  4. 67%
Explanation: First, find the total number of members in the club: 15+10=2515 + 10 = 25. Next, calculate the percentage of members who are in 7th grade by dividing the number of 7th graders by the total number of members and multiplying by 100: 1525×100%=0.60×100%=60%\frac{15}{25} \times 100\% = 0.60 \times 100\% = 60\%.

Question 9

A video game originally priced at $50 is on sale for 20% off. A week later, the store offers an additional 10% off the sale price. What is the final price of the game?

  1. $35.00
  2. $36.00 (correct answer)
  3. $40.00
  4. $45.00
Explanation: First, calculate the initial sale price. A 20% discount on $50 is (0.20 \times 50 = 10\). The sale price is \(50 - 10=10 = 40). Next, calculate the additional 10% discount on the sale price. A 10% discount on $40 is (0.10 \times 40 = 4\). The final price is \(40 - 4=4 = 36).

Question 10

A school library has 1,200 books. 45% of the books are fiction. Of the fiction books, 20% are science fiction. How many science fiction books are in the library?

  1. 108 (correct answer)
  2. 240
  3. 540
  4. 780
Explanation: First, find the number of fiction books: 1200×0.45=5401200 \times 0.45 = 540. Then, find the number of science fiction books, which is 20% of the fiction books: 540×0.20=108540 \times 0.20 = 108.

Question 11

A student estimated the length of a rope to be 80 cm. The actual length was 64 cm. What was the percent error of the student's estimate relative to the actual length?

  1. 16%
  2. 20%
  3. 25% (correct answer)
  4. 80%
Explanation: Percent error is calculated as ∣Estimated Value−Actual Value∣Actual Value×100%\frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \times 100\%. The error in measurement is ∣80−64∣=16|80 - 64| = 16 cm. The percent error is 1664×100%=14×100%=25%\frac{16}{64} \times 100\% = \frac{1}{4} \times 100\% = 25\%.

Question 12

A jacket is on sale for $60 after a 25% discount. What was the original price of the jacket?

  1. $45.00
  2. $75.00
  3. $80.00 (correct answer)
  4. $90.00
Explanation: The sale price of $60 represents 100% - 25% = 75% of the original price. Let P be the original price. The equation is (0.75 \times P = 60\). To find the original price, divide the sale price by 0.75: \(P = 60 \div 0.75 = $80).

Question 13

A family's dinner bill is $120. They want to leave a 20% tip on the bill before tax is added. The sales tax is 10% of the bill. What is the total amount they will pay?

  1. $156.00 (correct answer)
  2. $158.40
  3. $144.00
  4. $132.00
Explanation: First, calculate the tip: 20% of $120 is (0.20 \times 120 = 24\). Next, calculate the sales tax: 10% of $120 is \(0.10 \times 120 = 12). The total amount is the sum of the bill, the tip, and the tax: (120+120 + 24 + 12=12 = 156).

Question 14

A salesperson earns a monthly salary of $2,000 plus a 4% commission on all sales over $10,000. If their total sales for the month were $40,000, what were their total earnings for the month?

  1. $1,200
  2. $1,600
  3. $3,200 (correct answer)
  4. $3,600
Explanation: First, determine the amount of sales eligible for commission: (40,000−40,000 - 10,000 = 30,000\). Next, calculate the commission earned on this amount: 4% of $30,000 is \(0.04 \times 30000 = 1,200). Finally, add the salary to the commission for total earnings: (2,000+2,000 + 1,200 = $3,200).

Question 15

The population of a town was 8,000 in 2020. By 2021, the population had increased by 5%. What was the population of the town in 2021?

  1. 400
  2. 8,040
  3. 8,400 (correct answer)
  4. 12,000
Explanation: First, calculate the increase in population: 5% of 8,000 is 0.05×8000=4000.05 \times 8000 = 400. Then, add this increase to the original population: 8000+400=8,4008000 + 400 = 8,400. Alternatively, a 5% increase means the new population is 105% of the original: 8000×1.05=8,4008000 \times 1.05 = 8,400.

Question 16

A student's score on a test improved from 60 points to 75 points. What was the percent increase in the student's score?

  1. 15%
  2. 20%
  3. 25% (correct answer)
  4. 80%
Explanation: The formula for percent increase is New Value−Original ValueOriginal Value×100%\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%. The increase in score is 75−60=1575 - 60 = 15 points. The percent increase is 1560×100%=0.25×100%=25%\frac{15}{60} \times 100\% = 0.25 \times 100\% = 25\%.

Question 17

After a 20% price increase, the new price of a bicycle is $300. The store owner then offers a 10% discount on the new price. What was the original price of the bicycle before the increase?

  1. $240
  2. $250 (correct answer)
  3. $270
  4. $360
Explanation: The question asks for the original price, so the 10% discount is extra information not needed to solve the problem. Let the original price be P. The new price, $300, is 120% of the original price. The equation is (1.20 \times P = 300\). To find P, divide $300 by 1.20: \(P = 300 \div 1.2 = 250).

Question 18

The number of tickets sold for a play on Friday was 400. The number of tickets sold on Saturday was 25% more than on Friday. How many tickets were sold in total over the two days?

  1. 100
  2. 500
  3. 800
  4. 900 (correct answer)
Explanation: First, calculate the number of tickets sold on Saturday. The increase was 25% of 400, which is 0.25×400=1000.25 \times 400 = 100 tickets. So, on Saturday, 400+100=500400 + 100 = 500 tickets were sold. The total for the two days is the sum of Friday's and Saturday's sales: 400+500=900400 + 500 = 900 tickets.

Question 19

The price of a stock increased by 20% on Monday and then decreased by 20% on Tuesday. If the price of the stock was $100 at the start of Monday, what was its price at the end of Tuesday?

  1. $96 (correct answer)
  2. $99
  3. $100
  4. $104
Explanation: First, calculate the price after the 20% increase on Monday: (100×1.20=100 \times 1.20 = 120). Next, calculate the price after the 20% decrease on Tuesday. The decrease is based on the new price of 120: \(120 \times 0.20 = 24\). The final price is \(120 - $24 = $96).

Question 20

In a bag of 80 marbles, 25% are red. One-half of the remaining marbles are blue. How many marbles are blue?

  1. 20
  2. 30 (correct answer)
  3. 40
  4. 60
Explanation: First, calculate the number of red marbles: 25% of 80 is 0.25×80=200.25 \times 80 = 20. Next, find the number of remaining marbles: 80−20=6080 - 20 = 60. Finally, calculate the number of blue marbles, which is one-half of the remaining: 60÷2=3060 \div 2 = 30.