ISEE Lower Level Quantitative Reasoning Quiz
Practice Multi Step Word Problems in ISEE Lower 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 class is making friendship bracelets. Each bracelet requires 8 blue beads and 7 red beads. There are 24 students in the class, and each student will make one bracelet. If beads are sold in bags of 100, how many bags of beads must be purchased?
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 Lower 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 class is making friendship bracelets. Each bracelet requires 8 blue beads and 7 red beads. There are 24 students in the class, and each student will make one bracelet. If beads are sold in bags of 100, how many bags of beads must be purchased?
Explanation: First, find the total number of beads needed for one bracelet: 8 + 7 = 15 beads. Next, calculate the total number of beads needed for all 24 students: 15 beads/bracelet × 24 students = 360 beads. Finally, determine how many bags of 100 beads are needed: 360 ÷ 100 = 3 with a remainder of 60. Since they need 360 beads, they must purchase 4 bags to have enough.
A school library has 850 books. On Monday, 145 books are checked out. On Tuesday, a donation of 85 new books arrives. The remaining books are to be placed on empty shelves that can hold 30 books each. How many shelves will be completely filled?
Explanation: First, find the number of books after some are checked out: 850 - 145 = 705 books. Next, add the new books from the donation: 705 + 85 = 790 books. Finally, divide the total number of books by the shelf capacity: 790 ÷ 30 = 26 with a remainder of 10. The number of completely filled shelves is 26.
A train has 9 passenger cars, and each car can seat 60 people. On a trip from City A to City B, 7 cars were completely full and one car was exactly half full. The last car was empty. How many passengers were on the train?
Explanation: First, calculate the number of passengers in the 7 full cars: 7 cars × 60 people/car = 420 people. Next, calculate the number of passengers in the half-full car: 60 people ÷ 2 = 30 people. Finally, add the passengers from all the occupied cars to get the total: 420 + 30 = 450 passengers. The empty car and the total capacity of all cars are extra information.
If you need 60 balloons total and have 24, how many more are needed?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate how many more balloons are needed by subtracting what they have (24) from what they need (60). The correct answer works because it accurately calculates 60 - 24 = 36 using subtraction to find the difference. A common distractor fails because it results from adding instead of subtracting (60 + 24 = 84, choice A) or making computational errors. To help students, teach them to break down problems into smaller parts—identify that "how many more" always signals subtraction. Practice translating word phrases into operations and use estimation to check answers (60 - 24 should be close to 60 - 20 = 40).
The three fourth-grade classes at Elm School collected cans for a food drive. Ms. Davis's class collected 115 cans, Mr. Lee's class collected 128 cans, and Mrs. Gable's class collected 107 cans. If the students pack the cans into boxes that each hold 20 cans, how many cans will be left over?
Explanation: First, find the total number of cans collected by adding the amounts from the three classes: 115 + 128 + 107 = 350 cans. Next, divide the total number of cans by the number of cans each box can hold to find out how many full boxes can be made: 350 ÷ 20 = 17 with a remainder. To find the remainder, multiply the number of full boxes by the number of cans per box (17 × 20 = 340) and subtract this from the total: 350 - 340 = 10. There will be 10 cans left over.
If you need 48 cupcakes and have 18, how many more are needed?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate how many more cupcakes are needed by subtracting what they have (18) from what they need (48). The correct answer works because it accurately calculates 48 - 18 = 30 using subtraction to find the difference. A common distractor fails because it results from adding the numbers (48 + 18 = 66, choice B) instead of subtracting. To help students, teach them to break down problems into smaller parts—identify that "how many more" signals subtraction. Practice translating word problem phrases into mathematical operations, emphasizing that "more needed" means finding the difference between what's required and what's available.
Jada had 70 dollars, bought 2 puzzle sets at 18 dollars each and 4 stickers at 3 dollars each. How much money was left?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate the money left after buying puzzle sets and stickers, ensuring all steps are followed in logical sequence. The correct answer works because it accurately calculates 2 times 18 plus 4 times 3 as 48, then subtracts from 70 to get 22 using multiplication, addition, and subtraction. A common distractor fails because it results from miscalculating the sticker cost. To help students, teach them to break down problems into smaller parts—identify operations required for each step. Practice multi-step operations in different contexts, emphasizing order of operations and checking each step for accuracy. Encourage estimation as a check, not as a final answer.
A classroom needed 72 markers; markers came in packs of 8, and 3 packs were already there. How many more packs were needed?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate the additional packs of markers needed, ensuring all steps are followed in logical sequence. The correct answer works because it accurately calculates 72 divided by 8 as 9 packs total, then subtracts 3 to get 6 more using division and subtraction. A common distractor fails because it results from subtracting before dividing. To help students, teach them to break down problems into smaller parts—identify operations required for each step. Practice multi-step operations in different contexts, emphasizing order of operations and checking each step for accuracy. Encourage estimation as a check, not as a final answer.
Sofia had 100 dollars, bought 3 art kits at 24 dollars each and a 13-dollar sketchbook. How much money was left?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate the money left after buying art kits and a sketchbook, ensuring all steps are followed in logical sequence. The correct answer works because it accurately calculates 3 times 24 plus 13 as 85, then subtracts from 100 to get 15 using multiplication, addition, and subtraction. A common distractor fails because it results from miscalculating the kit total. To help students, teach them to break down problems into smaller parts—identify operations required for each step. Practice multi-step operations in different contexts, emphasizing order of operations and checking each step for accuracy. Encourage estimation as a check, not as a final answer.
For a party, 18 guests each got 2 slices of pizza; each pizza had 6 slices. How many pizzas were needed?
Explanation: This question tests lower-level ISEE quantitative reasoning skills, specifically solving multi-step problems using addition, subtraction, multiplication, and division. Multi-step word problems require understanding the problem context, identifying relevant numbers, and choosing the correct operations. In this specific scenario, students must calculate the number of pizzas needed for guests, ensuring all steps are followed in logical sequence. The correct answer works because it accurately calculates 18 times 2 as 36 slices, then divides by 6 to get 6 pizzas using multiplication and division. A common distractor fails because it results from dividing guests by slices per pizza without multiplying by slices per guest. To help students, teach them to break down problems into smaller parts—identify operations required for each step. Practice multi-step operations in different contexts, emphasizing order of operations and checking each step for accuracy. Encourage estimation as a check, not as a final answer.
Four friends shared the cost of a large pizza and a bottle of juice. The pizza cost 18andthejuicecost2. They paid with a $25 bill. If they split the change evenly among themselves, how much change did each friend receive?
Explanation: First, calculate the total cost of the food and drink: 18+2 = 20.Next,determinetheamountofchangetheyreceivedfromthe25 bill: 25−20 = 5.Finally,dividethechangeevenlyamongthefourfriends:5 ÷ 4 = $1.25 per friend.
Maria is reading a book that has 250 pages. She reads 20 pages each day from Monday to Friday. On Saturday and Sunday, she reads 30 pages each day. If she starts the book on a Monday, how many pages will she have left to read after one full week?
Explanation: First, calculate the number of pages read on weekdays: 5 days × 20 pages/day = 100 pages. Next, calculate the number of pages read on the weekend: 2 days × 30 pages/day = 60 pages. Then, find the total pages read in one week: 100 + 60 = 160 pages. Finally, subtract the pages read from the total number of pages in the book: 250 - 160 = 90 pages left to read.
A family drives 240 miles to the beach and back home along the same route. Their car can travel 30 miles on one gallon of gas. If gas costs $4 per gallon, what is the total cost of gas for the entire trip?
Explanation: First, calculate the total distance of the round trip: 240 miles × 2 = 480 miles. Next, determine the number of gallons of gas needed for the trip: 480 miles ÷ 30 miles/gallon = 16 gallons. Finally, calculate the total cost of the gas: 16 gallons × 4/gallon=64.
A baker has a recipe that makes 36 cookies. She bakes 3 batches. After the cookies cool, she gives 8 of them to her neighbor. She then packs the rest into bags of 6 cookies each. How many full bags of cookies can she make?
Explanation: First, calculate the total number of cookies baked: 36 cookies/batch × 3 batches = 108 cookies. Next, subtract the cookies given to the neighbor: 108 - 8 = 100 cookies. Finally, divide the remaining cookies by the number of cookies per bag: 100 ÷ 6 = 16 with a remainder of 4. Since the question asks for the number of full bags, the answer is 16.
David receives a 10allowanceeachweek.For4weeks,healsoearnsanextra5 each week for mowing the lawn. If he saves all this money, how much more does he need to buy a bicycle that costs $75?
Explanation: First, find David's total earnings per week: 10(allowance)+5 (mowing) = 15.Next,calculatehistotalsavingsover4weeks:15 × 4 = 60.Finally,subtracthistotalsavingsfromthecostofthebicycletofindouthowmuchmoremoneyheneeds:75 - 60=15.
A family has 200 books to pack for a move. A small box can hold 10 books, and a large box can hold 25 books. They completely fill 6 large boxes. How many small boxes will they need for the remaining books?
Explanation: This is a multi-step word problem that tests your ability to work through operations in the correct sequence and track what information you still need to find. Start by figuring out how many books are already packed. Since they completely fill 6 large boxes and each large box holds 25 books, multiply: 6×25=150 books are already packed. This means 200−150=50 books remain to be packed. Now you need to determine how many small boxes are required for these remaining 50 books. Since each small box holds 10 books, divide: 50÷10=5 small boxes needed. Looking at the wrong answers: Choice A (15 boxes) likely comes from dividing the total 200 books by 10, ignoring that 150 books are already packed in large boxes. Choice B (6 boxes) probably results from confusing the number of large boxes already used with the number of small boxes needed. Choice D (50 boxes) represents the number of remaining books, not the number of boxes needed—this shows a failure to complete the final division step. The correct answer is C (5 boxes). When solving multi-step word problems like this, always identify what you know, what you need to find, and work through each step systematically. Write down intermediate results (like "150 books packed" and "50 books remaining") to avoid losing track of your progress and ensure you're answering the actual question being asked.
A juice stand sold 120 cups of lemonade on Friday. On Saturday, it sold 20 more cups than on Friday. On Sunday, it sold half as many cups as it did on Saturday. How many cups of lemonade were sold in total over the three days?
Explanation: First, find the number of cups sold on Saturday: 120 + 20 = 140 cups. Next, find the number of cups sold on Sunday: 140 ÷ 2 = 70 cups. Finally, add the sales from all three days to find the total: 120 (Friday) + 140 (Saturday) + 70 (Sunday) = 330 cups.
At a school fair, tickets for games cost 2each.Sarahstartswith20. She buys a hot dog for $4 and then spends the rest of her money on game tickets. If each game requires one ticket, how many games can she play?
Explanation: This is a multi-step word problem that tests your ability to work backwards from a total amount of money through sequential purchases. When you see problems involving "spending money on different items," always track the remaining money after each purchase. Let's work through Sarah's spending step by step. She starts with 20andfirstbuysahotdogfor4. This leaves her with 20−4=16 dollars for game tickets. Since each game ticket costs $2, we divide her remaining money by the cost per ticket: 16÷2=8 tickets. Since each game requires one ticket, Sarah can play 8 games. Now let's examine why the other answers are wrong. Choice A (16 games) represents the trap of dividing Sarah's total starting money (20)bytheticketprice(2), ignoring that she spent 4onthehotdogfirst.ChoiceB(10games)mightresultfromincorrectlycalculatingherremainingmoneyas20 after buying the hot dog, then dividing by $2. Choice C (12 games) could come from subtracting the hot dog cost from the wrong starting point or making an arithmetic error in the division. The correct answer is D) 8 games. Study tip: In multi-step money problems, always work chronologically through each transaction. Calculate the remaining amount after each purchase before moving to the next step. Write down the amount remaining after each transaction to avoid mixing up your starting point for subsequent calculations.
A farmer has 15 rows of corn and 12 rows of tomatoes in a field. Each row of corn has 30 plants, and each row of tomatoes has 20 plants. How many more corn plants than tomato plants are in the field?
Explanation: This is a multi-step word problem that tests your ability to calculate totals and find differences. When you see questions asking "how many more," you need to find two separate quantities and subtract the smaller from the larger. First, calculate the total corn plants. You have 15 rows of corn with 30 plants each: 15×30=450 corn plants. Next, calculate the total tomato plants. You have 12 rows of tomatoes with 20 plants each: 12×20=240 tomato plants. Finally, find the difference: 450−240=210 more corn plants than tomato plants. Looking at the wrong answers: Choice A (690) represents adding the corn and tomato plants together instead of finding the difference. Choice B (240) is just the total number of tomato plants—you might get this if you forgot to subtract and only calculated one part. Choice C (450) is the total number of corn plants alone, which you'd get if you calculated the corn correctly but forgot to subtract the tomatoes. The key strategy for "how many more" problems is to remember they're asking for a difference, not a sum. Always calculate both quantities completely before subtracting. Also, double-check that your final answer makes logical sense—since there are more corn plants, the difference should be positive and reasonable given the numbers in the problem.
For a school assembly, 240 chairs are arranged in rows. The first 5 rows have 18 chairs each. The rest of the chairs are arranged in rows of 15. How many rows of 15 chairs are there?
Explanation: First, calculate the number of chairs in the first 5 rows: 5 rows × 18 chairs/row = 90 chairs. Next, subtract these chairs from the total to find how many chairs are left: 240 - 90 = 150 chairs. Finally, divide the remaining chairs by 15 to find the number of rows with 15 chairs: 150 ÷ 15 = 10 rows.