ISEE Middle Level Quantitative Reasoning Quiz
Practice Multi Step Word Problems in ISEE Middle Level Quantitative Reasoning with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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A farmer is building a straight fence that is 120 meters long. He places a fence post at the start of the fence and then a post every 3 meters. If each fence post costs $7, what is the total cost of all the fence posts needed?
This quiz focuses on Multi Step Word Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Middle Level Quantitative Reasoning.
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.
A farmer is building a straight fence that is 120 meters long. He places a fence post at the start of the fence and then a post every 3 meters. If each fence post costs $7, what is the total cost of all the fence posts needed?
Explanation: First, determine the number of 3-meter sections in the fence: (120 \text{ meters} \div 3 \text{ meters/section} = 40) sections. For a straight fence with posts at both ends, the number of posts is one more than the number of sections. So, the farmer needs (40 + 1 = 41) posts. Finally, calculate the total cost of the posts: (41 \text{ posts} \times $7/\text{post} = $287).
A school is planning a field trip for 130 students and 12 adults. Each bus can hold a maximum of 48 people. What is the total number of empty seats on all the buses used for the trip?
Explanation: First, find the total number of people going on the trip: (130 + 12 = 142) people. Next, determine the minimum number of buses needed by dividing the total people by the bus capacity: (142 \div 48 = 2) with a remainder of 46. Since there is a remainder, 3 buses are needed. Then, calculate the total number of seats on 3 buses: (3 \times 48 = 144) seats. Finally, subtract the number of people from the total number of seats to find the number of empty seats: (144 - 142 = 2).
To earn an A in science, Jordan needs an average of at least 92 on five tests. His scores on the first four tests are 88, 95, 86, and 94. What is the minimum score Jordan must get on the fifth test to earn an A?
Explanation: First, find the total score Jordan needs across all five tests to have an average of 92. This is (5 \times 92 = 460). Next, find the sum of his scores on the first four tests: (88 + 95 + 86 + 94 = 363). Finally, subtract the sum of the first four scores from the target total score to find the required score on the fifth test: (460 - 363 = 97).
A charity fundraiser receives donations from 120 people. The average donation is 25.Alocalcompanyagreestomatcheverydollardonatedaboveatotalof2,000. How much money will the company donate?
Explanation: First, calculate the total amount of money donated by the people: (120 \text{ people} \times $25/\text{person} = $3,000). The company matches the amount donated above 2,000. To find this amount, subtract the threshold from the total donations: \(\3,000 - $2,000 = $1,000). The company will donate this matched amount, which is $1,000.
A recipe for 6 servings uses 1.50 cups rice and 3.00 cups broth; what are the adjusted ingredient amounts for 15 servings?
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must scale a recipe from 6 to 15 servings, executing calculations in the correct order. The correct answer is achieved by finding the scaling factor (15 ÷ 6 = 2.5), then multiplying each ingredient: rice (1.50 × 2.5 = 3.75 cups) and broth (3.00 × 2.5 = 7.50 cups). A common distractor might involve using an incorrect scaling factor or only scaling one ingredient. To help students: Teach them to always find the ratio of new servings to original servings first, then apply this factor consistently to all ingredients.
A bag of 96 candies is to be shared among three friends: Amy, Beth, and Carla. Amy gets (\frac{1}{4}) of the candies. Beth gets (\frac{1}{3}) of the remaining candies. Carla gets the rest. How many more candies does Carla get than Amy?
Explanation: First, find how many candies Amy gets: (96 \times \frac{1}{4} = 24) candies. Next, find the number of remaining candies: (96 - 24 = 72) candies. Then, find how many candies Beth gets from the remainder: (72 \times \frac{1}{3} = 24) candies. Carla gets the rest, which is (72 - 24 = 48) candies. Finally, find the difference between Carla's and Amy's shares: (48 - 24 = 24) candies.
An employee earns $15 per hour for the first 40 hours worked in a week. For any hours worked over 40, the employee earns 1.5 times the regular hourly rate. If the employee worked 46 hours in one week, what were their total earnings for that week?
Explanation: First, calculate the earnings for the first 40 hours: (40 \text{ hours} \times $15/\text{hour} = $600). Next, determine the number of overtime hours: (46 - 40 = 6) hours. Then, calculate the overtime rate: ($15 \times 1.5 = $22.50) per hour. Calculate the overtime earnings: (6 \text{ hours} \times $22.50/\text{hour} = $135). Finally, add the regular earnings and overtime earnings: ($600 + $135 = $735.00).
A recipe for a batch of cookies requires (\frac{3}{4}) cup of sugar. Liam wants to make 3 batches of cookies. He starts with a bag containing 4 cups of sugar. After making the cookies, how much sugar is left in the bag?
Explanation: First, calculate the total amount of sugar needed for 3 batches. This is (3 \times \frac{3}{4} = \frac{9}{4}) cups. Convert the improper fraction to a mixed number: (\frac{9}{4} = 2 \frac{1}{4}) cups. Then, subtract the amount of sugar used from the initial amount: (4 - 2 \frac{1}{4} = 1 \frac{3}{4}) cups.
A school bake sale sells brownies for 1.50eachandcookiesfor0.75 each. The ingredients cost a total of $45. If they sell 60 brownies and 80 cookies, what is the total profit from the bake sale?
Explanation: First, calculate the total revenue from selling brownies: (60 \times $1.50 = $90). Next, calculate the total revenue from selling cookies: (80 \times $0.75 = $60). Then, find the total revenue: ($90 + $60 = $150). Finally, calculate the profit by subtracting the cost of ingredients from the total revenue: (Profit = Revenue - Cost = $150 - $45 = $105).
Maya withdrew some money from her bank account. She spent 35onashirt.Thenshegavehalfoftheremainingmoneytoherbrother.Ifshehas40 left, how much money did she withdraw from her account originally?
Explanation: This problem is best solved by working backward. Maya has 40 left after giving half of her money to her brother. So, before giving him money, she had \(\40 \times 2 = $80). Before that, she spent 35 on a shirt. To find the amount she had before the purchase, add that amount back: \(\80 + $35 = $115). This was the amount she originally withdrew.
You have a 250.00eventbudget;youpay85.00 for a venue, 9.50perpersonfor12guests,and30.00 for music. What is the final budget after all expenses?
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must interpret an event budget scenario with multiple expenses, executing calculations in the correct order. The correct answer is achieved by calculating total expenses: venue (85.00)+catering(9.50 × 12 = 114.00)+music(30.00) = 229.00,thensubtractingfromthebudget(250.00 - 229.00=21.00). A common distractor might involve forgetting to multiply the per-person cost by the number of guests or adding instead of subtracting expenses. To help students: Teach them to list all expenses separately, perform any multiplication first, then sum all costs before subtracting from the total budget.
A road trip has legs of 120 miles, 85 miles, and 95 miles; at 25 miles per gallon, how much fuel is needed for the entire trip?
Explanation: This question tests ISEE Middle Level quantitative reasoning skills, specifically solving multi-step word problems using the four operations. Multi-step problems require students to apply the correct sequence of operations to reach a logical solution, often requiring addition, subtraction, multiplication, and division. In this problem, students must interpret a road trip scenario with multiple legs and fuel efficiency, executing calculations in the correct order. The correct answer is achieved by first finding the total distance (120 + 85 + 95 = 300 miles), then dividing by the fuel efficiency (300 ÷ 25 = 12 gallons). A common distractor might involve dividing individual legs by the fuel efficiency separately or confusing miles with gallons. To help students: Teach them to identify what the question asks for (total fuel), combine all distances first, then apply the fuel efficiency calculation as a final step.
A jacket is originally priced at $80. It is on sale for 25% off. A customer has an additional coupon for 10% off the sale price. How much does the customer pay for the jacket, before tax?
Explanation: First, calculate the sale price after the 25% discount. The discount amount is (0.25 \times $80 = $20). The sale price is ($80 - $20 = $60). Next, calculate the additional 10% off the sale price. The coupon discount is (0.10 \times $60 = $6). The final price is ($60 - $6 = $54.00).
A group of 4 friends buys 2 large pizzas at 14.50eachand4drinksat2.25 each. If they split the total cost equally, how much does each friend pay?
Explanation: First, calculate the total cost of the pizzas: (2 \times $14.50 = $29.00). Next, calculate the total cost of the drinks: (4 \times $2.25 = $9.00). Then, find the total cost of the entire meal: ($29.00 + $9.00 = $38.00). Finally, divide the total cost by the number of friends to find the cost per person: ($38.00 \div 4 = $9.50).
A printer can print 240 pages in 8 minutes. The printer jams and is stopped for 5 minutes. After the jam is cleared, it prints another 300 pages at the same rate. What is the total time, in minutes, from the start of printing to the end?
Explanation: First, find the printing rate: (240 \text{ pages} \div 8 \text{ minutes} = 30) pages per minute. Next, find the time it takes to print the second batch of 300 pages: (300 \text{ pages} \div 30 \text{ pages/minute} = 10) minutes. Finally, add all the time segments together: (8 \text{ minutes} + 5 \text{ minutes} + 10 \text{ minutes} = 23) minutes.
A factory produces 1,500 toy cars in a shift. The cars are packed into boxes that hold 24 cars each. The filled boxes are then packed into crates that hold 10 boxes each. How many toy cars are left over that do not make up a full crate?
Explanation: First, find the number of full boxes that can be packed: (1,500 \div 24 = 62.5). This means 62 full boxes and (0.5 \times 24 = 12) leftover cars. Next, find how many full crates can be made from the 62 boxes: (62 \div 10 = 6.2). This means 6 full crates and 2 leftover boxes. The cars left over that do not make up a full crate are the cars in the 2 leftover boxes plus the 12 loose cars. The number of cars is ((2 \text{ boxes} \times 24 \text{ cars/box}) + 12 \text{ cars} = 48 + 12 = 60) cars.
A library charges a fine of 0.25perdayforanoverduebook.Forabookthatismorethan10daysoverdue,thereisanadditionalflatfeeof5.00. If a book is returned 18 days overdue, what is the total fine?
Explanation: First, calculate the daily fine for the entire overdue period: (18 \text{ days} \times $0.25/\text{day} = $4.50). Since the book is 18 days overdue, which is more than 10 days, the additional 5.00 flat fee applies. Add the daily fine and the flat fee to find the total fine: \(\4.50 + $5.00 = $9.50).
The temperature in a town was -8°F at 6:00 AM. The temperature rose by 3°F each hour for the next 5 hours. Then, it dropped by 12°F over the next 6 hours. What was the temperature at 5:00 PM?
Explanation: First, calculate the total temperature increase over the first 5 hours: (5 \text{ hours} \times 3°F/\text{hour} = 15°F). Then, calculate the temperature at 11:00 AM (5 hours after 6:00 AM): (-8°F + 15°F = 7°F). Finally, calculate the temperature at 5:00 PM (6 hours later) after it dropped by 12°F: (7°F - 12°F = -5°F).
At a carnival, Ben won 12 tickets. Sarah won twice as many tickets as Ben. Marco won 8 fewer tickets than Sarah. How many tickets did they win in total?
Explanation: First, find the number of tickets Sarah won: (12 \times 2 = 24) tickets. Next, find the number of tickets Marco won: (24 - 8 = 16) tickets. Finally, add the number of tickets each person won to find the total: (12 \text{ (Ben)} + 24 \text{ (Sarah)} + 16 \text{ (Marco)} = 52) tickets.
A rectangular garden is 12 feet long and 8 feet wide. The owner wants to cover the garden with topsoil that costs 3persquarefoot.Theownerhasabudgetof300 for the topsoil. How much money will be left after buying the topsoil?
Explanation: First, calculate the area of the garden: (Area = length \times width = 12 \text{ ft} \times 8 \text{ ft} = 96 \text{ sq ft}). Next, calculate the total cost of the topsoil: (96 \text{ sq ft} \times $3/\text{sq ft} = $288). Finally, subtract the cost from the budget to find the remaining money: ($300 - $288 = $12).