- 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?
Answer: 26 shelves
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 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?
Answer: 4 bags
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 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?
Answer: 5 boxes
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 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?
Answer: 16 bags
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.
- At a carnival, a ring toss game costs 3 tickets to play. A water balloon game costs 2 tickets. Ben has 25 tickets. He plays the ring toss 3 times. How many times can he play the water balloon game with his remaining tickets?
Answer: 8 times
This is a multi-step word problem that tests your ability to work with subtraction and division in a real-world context. When you see problems involving "remaining" amounts, you'll need to calculate what's used first, then work with what's left.
Let's work through this step by step. Ben starts with 25 tickets and plays ring toss 3 times at 3 tickets per game. First, calculate how many tickets he uses: 3×3=9 tickets spent on ring toss. Next, find his remaining tickets: 25−9=16 tickets left. Finally, determine how many water balloon games he can play: 16÷2=8 games, since each water balloon game costs 2 tickets.
Looking at the wrong answers: Choice A (16 times) represents the number of tickets Ben has left, not the number of games he can play. This is a common trap—always check what the question is actually asking for. Choice B (9 times) is the number of tickets Ben spent on ring toss, showing confusion between tickets used and games playable. Choice C (12 times) might come from incorrectly calculating 25−3=22 remaining tickets, then 22÷2=11 (rounded to 12), mixing up the cost per ring toss game.
The correct answer is D (8 times).
Study tip: In multi-step problems, write down each calculation clearly. First find what's used, then what remains, then what you can do with the remainder. Always double-check that your final answer matches what the question asks for. - If you need 48 cupcakes and have 18, how many more are needed?
Answer: 30
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.
- 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?
Answer: 330 cups
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.
- If you need 60 balloons total and have 24, how many more are needed?
Answer: 36
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).
- Four friends shared the cost of a large pizza and a bottle of juice. The pizza cost $18 and the juice cost $2. They paid with a $25 bill. If they split the change evenly among themselves, how much change did each friend receive?
Answer: $1.25
First, calculate the total cost of the food and drink: $18 + $2 = $20. Next, determine the amount of change they received from the $25 bill: $25 - $20 = $5. Finally, divide the change evenly among the four friends: $5 ÷ 4 = $1.25 per friend.
- Sofia had 100 dollars, bought 3 art kits at 24 dollars each and a 13-dollar sketchbook. How much money was left?
Answer: $15
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.
- At a school fair, tickets for games cost $2 each. Sarah starts with $20. 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?
Answer: 8 games
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 $20 and first buys a hot dog for $4. 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) by the ticket price ($2), ignoring that she spent $4 on the hot dog first. Choice B (10 games) might result from incorrectly calculating her remaining money as $20 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. - If you need 36 plates total and have 14, how many more are needed?
Answer: 22
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 plates are needed by subtracting what they have (14) from what they need (36). The correct answer works because it accurately calculates 36 - 14 = 22 using subtraction to find the difference. A common distractor fails because it results from subtracting in the wrong order (14 - 36) or adding instead of subtracting (36 + 14 = 50, choice A). To help students, teach them to break down problems into smaller parts—identify the total needed and what's already available. Practice setting up subtraction problems correctly (larger number - smaller number) and using estimation to check if answers are reasonable.
- 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?
Answer: 10 cans
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.
- A soccer team of 14 players is selling candy bars for a fundraiser. Each player was given a box of 25 candy bars to sell. At the end of the fundraiser, the team had a total of 40 unsold candy bars. How many candy bars did the team sell in total?
Answer: 310 candy bars
First, calculate the total number of candy bars the team had to sell: 14 players × 25 candy bars/player = 350 candy bars. Next, subtract the number of unsold candy bars from the total to find the number of candy bars sold: 350 - 40 = 310 candy bars.
- How many packs of markers are needed for 30 students if each pack has 5?
Answer: 6 packs
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 packs of markers are needed for 30 students when each pack contains 5 markers, assuming each student needs one marker. The correct answer works because it accurately calculates 30 ÷ 5 = 6 using division to find the number of packs needed. A common distractor fails because it results from subtracting instead of dividing (30 - 5 = 25, choice B) or confusing the operation entirely. To help students, teach them to break down problems into smaller parts—recognize that "packs of" problems typically involve division. Practice identifying when to divide the total by the group size, and verify answers by multiplying back (6 packs × 5 markers = 30 markers).
- Leo earned $15 for mowing a lawn. He also gets a $5 allowance every week. If he starts with no money and wants to buy a video game that costs $48, how many weeks must he get his allowance in addition to the money from mowing the lawn?
Answer: 7 weeks
First, subtract the money Leo earned from mowing from the total cost of the video game to see how much more he needs: $48 - $15 = $33. Next, divide this remaining amount by his weekly allowance to find out how many weeks it will take: $33 ÷ $5 = 6.6 weeks. Since Leo cannot receive a partial week's allowance, he must wait for 7 complete weeks to have enough money ($15 + $35 = $50, which is more than the $48 needed).
- A classroom needed 72 markers; markers came in packs of 8, and 3 packs were already there. How many more packs were needed?
Answer: 6
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.
- For a class party, a teacher buys 5 large pizzas. Each pizza is cut into 12 slices. If there are 28 students in the class and each student eats 2 slices, how many pizza slices will be left over?
Answer: 4 slices
First, calculate the total number of pizza slices: 5 pizzas × 12 slices/pizza = 60 slices. Next, calculate the total number of slices the students will eat: 28 students × 2 slices/student = 56 slices. Finally, subtract the number of slices eaten from the total number of slices to find the amount left over: 60 - 56 = 4 slices.
- A box contains 3 bags of red marbles and 4 bags of blue marbles. Each bag of red marbles has 25 marbles. Each bag of blue marbles has 30 marbles. If a student takes 15 marbles out of the box, how many marbles are left?
Answer: 180 marbles
This is a multi-step word problem that requires you to find the total number of marbles first, then subtract what was taken. When you see problems with multiple groups of items, always organize the information systematically.
Start by calculating the total marbles in the box. For red marbles: 3 bags × 25 marbles per bag = 75 red marbles. For blue marbles: 4 bags × 30 marbles per bag = 120 blue marbles. The total is 75 + 120 = 195 marbles in the box.
Since 15 marbles were taken out, subtract: 195 - 15 = 180 marbles remaining.
Let's examine why the other answers are wrong. Choice A (225 marbles) represents a calculation error where someone might have added 15 instead of subtracting it, or miscalculated the initial total. Choice B (195 marbles) is the total number of marbles before any were removed - this is what you'd get if you forgot the final subtraction step entirely. Choice C (210 marbles) could result from incorrectly calculating the initial total, perhaps by using wrong numbers for marbles per bag.
The key strategy here is to work methodically: first find the total of each type of marble, then add them together for the overall total, and finally perform the subtraction. Always double-check that you've answered the actual question being asked - in this case, how many are left after removal, not how many were there originally.
- 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?
Answer: 210 plants
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.
