All questions
Question 1
At a mall, Jordan buys a 12 notebook and a 20 hoodie with 25% off. The store charges 8% sales tax on the discounted total. A 15 hat is full price, but Jordan does not buy it. Jordan also has a 5 gift card to use. Which steps are necessary to find the final amount Jordan pays?
- Add the original prices, then subtract 25% at the end
- Ignore the hat, discount hoodie, add items, apply tax, use gift card (correct answer)
- Apply tax first, then take 25% off the taxed total
- Use the hat price to estimate, then add the gift card value
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, Jordan buys a notebook (12)andahoodie(20 with 25% off), pays 8% tax on the discounted total, and uses a $5 gift card - the $15 hat is irrelevant since it's not purchased. Choice B is correct because it accurately identifies the steps: ignore the unpurchased hat, discount the hoodie (25% off $20 = $5 off, so 15),addthenotebookanddiscountedhoodie(12 + $15 = 27),apply827 × 1.08 = 29.16),thensubtractthegiftcard(29.16 - $5 = $24.16). Choice A incorrectly suggests discounting the total at the end rather than just the hoodie, while Choice C wrongly applies tax before the discount. To help students: teach them to identify what's actually purchased versus what's just mentioned, practice breaking down multi-step problems systematically, and emphasize reading carefully for specific discount applications. Question 2
For a bake sale, students make 60 cupcakes and sell them for 1.50 each. Ingredients cost 28, and table rental costs 12. They also print 20 flyers for 0.10 each. A talent show was planned but not held. What data is irrelevant to solving this question?
- The planned talent show that was not held (correct answer)
- The ingredient cost and the table rental cost
- The number of cupcakes and price per cupcake
- The flyer cost and number of flyers printed
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. For the bake sale profit calculation, we need revenue (60 × $1.50 = $90) minus costs (ingredients $28 + table $12 + flyers 20 × $0.10 = $2, total $42), giving $48 profit. Choice A is correct because the planned but not held talent show is completely irrelevant to the bake sale calculations - it doesn't affect revenue or costs. Choices B, C, and D all identify information that is actually needed: ingredient and table costs affect expenses, cupcake count and price determine revenue, and flyer costs are part of expenses. To help students: teach them to identify what actually happened versus what was merely planned, practice distinguishing between related and unrelated events, and emphasize focusing on the specific activity being analyzed.
Question 3
A class buys 4 science kits at $18 each and gets 15% off the kits. Shipping is $12, and tax is 5% on the discounted kits only. A different kit costs $25 but is out of stock. The teacher brings 10 markers from home. Which details are critical to finding the answer?
- Out-of-stock kit price and number of markers brought
- Kit count and price, discount rate, shipping, and tax rule (correct answer)
- Only the 5% tax rate and the $12 shipping fee
- Add shipping to kits first, then take 15% off everything
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. The class's total cost requires: kit cost (4 × $18 = 72),apply1572 × 0.85 = 61.20),addshipping(12), apply 5% tax to discounted kits only ($61.20 × 0.05 = $3.06), for a total of $61.20 + $12 + $3.06 = $76.26. Choice B is correct because it identifies all critical components: kit count and price for the base cost, discount rate for savings, shipping as an additional cost, and the tax rule specifying tax applies only to discounted kits. Choice A incorrectly includes irrelevant information about out-of-stock items and markers, Choice C omits crucial kit information, and Choice D suggests an incorrect calculation sequence. To help students: teach careful reading of tax and discount applications, emphasize identifying what's actually purchased versus mentioned, and practice multi-step problems with conditional rules. Question 4
Leah buys 3 pens at $2 each and a binder for $8. She has a coupon for 10% off the binder only. Sales tax is 6% on the total after the coupon. A notebook costs $5 but she leaves it behind. What is the first step in solving this problem?
- Apply 6% tax to $8 before using the coupon
- Ignore the notebook and find the binder's discounted price (correct answer)
- Add the notebook price to make the total more accurate
- Round all prices to the nearest $10 for easier math
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. Leah's purchase involves pens (3 × $2 = 6),abinder(8 with 10% off), and 6% tax on the discounted total - the unpurchased notebook is irrelevant. Choice B is correct as the first step because it properly identifies ignoring the unpurchased notebook and focusing on finding the binder's discounted price (10% off $8 = $0.80 off, so $7.20). Choice A incorrectly suggests applying tax before the coupon discount, Choice C wrongly includes the unpurchased notebook, and Choice D suggests unnecessary rounding. To help students: teach them to identify the logical sequence of operations (discounts before tax), emphasize reading for what's actually purchased, and practice breaking complex problems into ordered steps starting with identifying relevant items. Question 5
A builder needs 30 wooden boards at $4 each and 2 buckets of nails at $9 each. A different type of board costs $6 each but is not used. Delivery is a flat $15 fee. The work will take about 3 hours. Which details are critical to finding the total material cost?
- Include the 3 hours to convert time into dollars
- Use only the $6 boards because they cost more
- Boards used, nail buckets, and the $15 delivery fee (correct answer)
- Add all board types, then remove the unused ones later
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. The builder's material cost includes only what's actually used: 30 boards at 4each(120), 2 nail buckets at 9each(18), and the $15 delivery fee - the $6 boards and work time are irrelevant. Choice C is correct because it identifies exactly these three cost components: boards used + nail buckets + delivery fee = $120 + $18 + $15 = $153. Choice A incorrectly suggests including work time in material costs, Choice B focuses on unused expensive boards, and Choice D suggests an inefficient approach of adding then subtracting. To help students: teach them to distinguish between material costs and labor time, emphasize reading for what's actually purchased versus what's merely mentioned, and practice categorizing different types of expenses in construction problems. Question 6
A flight lasts 3 hours 20 minutes, then there is a 1 hour 5 minute layover. The next flight lasts 1 hour 40 minutes. The airport has a 9 AM yoga class and a $7 smoothie. Which steps are necessary to find the total trip time?
- Add both flight durations and the layover duration (correct answer)
- Add yoga class time to the first flight duration
- Subtract layover time from the second flight duration
- Convert smoothie cost into minutes, then add
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem involves flights, layovers, and unrelated airport activities. Choice A is correct because adding both flight durations and the layover provides the steps to find total trip time. Choice B is incorrect because adding yoga class time confuses activities with travel, a common error in sequencing. To help students: Teach them to focus on transit elements, convert all to minutes for addition, and ignore non-travel events. Watch for: students subtracting instead of adding or mixing costs with times.
Question 7
Ella buys a $9 book and a $15 game. The game is 20% off, and sales tax is 8% on the discounted subtotal. A $6 magazine is on the shelf, and the cashier's name is Sam. What information do you need to solve this problem?
- Book price, game price, discount rate, and tax rate (correct answer)
- Magazine price and cashier's name
- Cashier's name and tax rate
- Magazine price and discount rate
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem involves buying items with discounts, taxes, and unrelated details like a magazine and cashier name. Choice A is correct because book price, game price, discount rate, and tax rate are essential for computing the total payment. Choice B is incorrect because magazine price and cashier's name are irrelevant, a common mistake when including all mentioned elements. To help students: Teach them to identify cost-affecting factors, ignore personal or unrelated facts, and practice subtotal calculations. Watch for: students confusing shelf items with purchases or skipping discount applications.
Question 8
At a bake sale, the class sells 45 cupcakes for $2 each and 30 cookies for $1 each. Ingredients cost $38 total, and they rent a table for $12. A DJ offers music for $20, but they do not hire one. What data is irrelevant to solving this question?
- Cupcake price and number sold
- Cookie price and number sold
- DJ music cost that was not used (correct answer)
- Ingredient cost and table rental fee
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem details a bake sale with sales, costs, and an unused service offer. Choice C is correct because the DJ music cost that was not used is irrelevant to calculating profit from actual sales and expenses. Choice D is incorrect because ingredient and table costs are essential, not irrelevant, a common confusion when distinguishing used versus unused elements. To help students: Teach them to separate actual from potential costs, list revenues and expenses clearly, and verify irrelevance by checking impact on the total. Watch for: students mistakenly excluding necessary costs or including unpursued options.
Question 9
For a school fundraiser, the band sells 200 tickets at $4 each. Renting speakers costs $110, and printing tickets costs $25. They also plan a halftime game, but it is free to play. Which steps are necessary to find the fundraiser profit?
- Add all costs, then divide by 200
- Multiply ticket price by tickets sold, then subtract total expenses (correct answer)
- Add the free game value to revenue, then subtract expenses
- Subtract expenses from ticket price, then multiply by 200
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem details a ticket-selling fundraiser with expenses and a free activity. Choice B is correct because multiplying ticket price by tickets sold, then subtracting expenses, finds profit accurately. Choice C is incorrect because adding the free game's value assumes revenue, a common misinterpretation. To help students: Teach them to calculate revenue from sales, list and sum expenses, then subtract. Watch for: students incorporating free elements as costs or revenues incorrectly.
Question 10
To build a small garden bed, Nina buys 6 bags of soil at $4.50 each and 12 bricks at $1.25 each. The store offers 15% off bricks only, and delivery is $10. She also looks at $30 stepping stones but buys none. Which steps are necessary to find the total cost?
- Add soil and brick costs, then subtract 15% from the total
- Discount only the bricks, add soil, then add delivery fee (correct answer)
- Add delivery fee, then apply 15% off everything
- Include stepping stone price, then add delivery fee
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem details garden purchases with item-specific discounts, delivery, and unpurchased items. Choice B is correct because it sequences discounting only the bricks, adding soil, and including delivery to find the total cost accurately. Choice D is incorrect because it includes the unpurchased stepping stones, a common error when students add all listed prices without filtering. To help students: Teach them to apply discounts selectively, list steps in order like discount then add fees, and cross out irrelevant items. Watch for: students applying discounts broadly or forgetting additional fees like delivery.
Question 11
On a shopping trip, Maya buys a 12 notebook and a 20 hoodie. The store gives 25% off clothing and charges 6% sales tax on the discounted total. A poster costs 15 but she does not buy it, and socks were originally 8. Which steps are necessary to find the final amount Maya pays?
- Add all original prices, then subtract 25%
- Discount the hoodie, add notebook, then apply 6% tax (correct answer)
- Apply 6% tax first, then take 25% off
- Include the poster price because it is listed
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem provides details about a shopping trip where discounts and taxes are involved, including items bought and not bought. Choice B is correct because it accurately identifies the steps needed to calculate the total cost by focusing on discounting the hoodie, adding the notebook, and applying tax, while ignoring irrelevant items like the poster and socks. Choice A is incorrect because it suggests adding all original prices including unpurchased items, a common mistake when students fail to filter out extraneous data. To help students: Teach them to underline or highlight relevant data, practice breaking down problems into smaller steps, and encourage logical sequencing of operations. Watch for: students including unnecessary data or skipping critical steps like applying discounts before taxes.
Question 12
A bus route has stops every 0.8 miles along a 12-mile route. The bus travels at 25 mph between stops and spends 2 minutes at each stop (including the first and last stops). To find the total trip time, which calculation is NOT needed?
- The number of stops along the route
- The total time spent stopped at all stops
- The time spent traveling between stops
- The average speed including stop time (correct answer)
- The distance between consecutive stops
Explanation: When tackling multi-step word problems, you need to identify which pieces of information are actually required to solve the problem. This question tests whether you can distinguish between necessary calculations and extra information.
To find the total trip time, you need three key calculations. First, you must find the number of stops along the route (A) by dividing 12 miles by 0.8 miles per stop, which gives you 15 stops. Second, you need the total time spent stopped at all stops (B) by multiplying 15 stops by 2 minutes each, equaling 30 minutes. Third, you need the time spent traveling between stops (C) by calculating the distance traveled (12 miles) divided by speed (25 mph), which equals 0.48 hours or about 29 minutes. Adding the stopped time and traveling time gives you the total trip time.
However, the average speed including stop time (D) is not needed for this calculation. This would be something you might calculate after finding the total trip time, not something required to find it. Choice A is wrong because you must know how many stops exist to calculate stop time. Choice B is wrong because the total stopped time is a major component of the final answer. Choice C is wrong because traveling time between stops is the other major component needed.
Remember: when a question asks what's "NOT needed," identify what the problem is actually asking for, then eliminate any calculation that would be a result of your work rather than a step toward it.
Question 13
At the mall, Keisha buys a $40 jacket and a $18 shirt. The jacket is 30% off, and the tax is 9% on the discounted subtotal. A hat costs $14 but she does not buy it, and the food court opens at 11. Which details are critical to finding the amount she pays?
- Jacket and shirt prices, discount rate, and tax rate (correct answer)
- Hat price and food court opening time
- Food court opening time and tax rate
- Hat price and jacket discount rate
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem involves mall purchases with discounts, taxes, and unpurchased or timed details. Choice A is correct because jacket and shirt prices, discount rate, and tax rate are critical for the payment amount. Choice B is incorrect because hat price and food court time are irrelevant, a common inclusion of all mentioned items. To help students: Teach them to list purchased items, apply discounts to specifics, and compute subtotals before tax. Watch for: students adding unpurchased goods or confusing times with costs.
Question 14
A trip includes a 55-minute subway ride, then a 15-minute walk to the gate. The ferry ride is 1 hour 25 minutes. The schedule also lists a 2 PM dolphin talk. What is the first step in solving this problem?
- Decide if the dolphin talk should be counted as travel time
- Add the subway ride, walking time, and ferry ride durations (correct answer)
- Subtract the walking time from the ferry duration
- Convert 2 PM into minutes and add it
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem details a multi-mode trip with times and a scheduled talk. Choice B is correct because adding the subway ride, walking time, and ferry ride durations is the first step to total time. Choice A is incorrect because deciding on the dolphin talk as travel time confuses events, a common sequencing error. To help students: Teach them to sum transit durations in order, convert to consistent units, and exclude scheduled non-transit activities. Watch for: students subtracting walks or adding event times inappropriately.
Question 15
A carpenter charges $50 for the first hour and $35 for each additional hour. He also charges $20 for materials per project regardless of time. If a project takes 4.5 hours, which expression correctly calculates the total cost?
- $50 + $35(4.5) + $20
- $50 + $35(3.5) + $20 (correct answer)
- $50 + $35(4) + $20
- ($50 + $35)(4.5) + $20
- $50(1) + $35(3.5) + $20
Explanation: When you encounter word problems involving different rates or fees, the key is to carefully break down each component and identify what applies to which portion of the work.
The carpenter's pricing structure has three parts: $50 for the first hour, $35 for each additional hour beyond the first, and a flat $20 materials fee. For a 4.5-hour project, you need to separate the first hour from the remaining time.
The correct calculation is: $50 (first hour) + $35(3.5) (additional hours) + $20 (materials). Since the project takes 4.5 hours total, the additional time beyond the first hour is 4.5 - 1 = 3.5 hours. This matches choice B.
Choice A incorrectly multiplies $35 by the total project time (4.5 hours) instead of just the additional hours. This double-counts the first hour by charging both the $50 first-hour rate and including that hour again in the $35 calculation.
Choice C rounds 3.5 additional hours down to 4, which understates the actual additional time worked. The carpenter would charge for the full 3.5 hours, not just 4 whole hours.
Choice D adds the hourly rates together ($50 + $35) and multiplies by total time, completely misunderstanding the pricing structure. This treats both rates as applying to all hours worked.
Study tip: In multi-rate problems, always identify what triggers each rate. Here, only the first hour gets the $50 rate, while subsequent hours get the $35 rate. Draw a timeline if it helps visualize how the rates apply to different time periods.
Question 16
A plane leaves at 9:10 AM and lands at 11:00 AM. After a 50-minute layover, the next flight takes 2 hours 15 minutes. Jordan eats lunch at 12:30 PM and buys a $4 snack. What information do you need to solve this problem?
- Lunch time and snack cost
- First flight time, layover length, and second flight duration (correct answer)
- Snack cost and second flight duration
- Departure time and lunch time only
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem involves flight times, layovers, and unrelated activities like eating lunch or buying snacks. Choice B is correct because it focuses on the first flight time, layover length, and second flight duration, which are essential for calculating total travel time. Choice A is incorrect because it prioritizes irrelevant details like lunch time and snack cost, a common mistake when students confuse ancillary events with core travel components. To help students: Teach them to identify the main goal, such as total time, and map out timelines, while practicing to exclude non-essential facts. Watch for: students adding unrelated times or overlooking layovers in sequencing.
Question 17
Noah buys 2 movie tickets at $11 each and a $6 popcorn. A coupon takes $3 off the popcorn only, and tax is 4% on the final subtotal. A candy costs $2 but he skips it, and the movie starts at 7:45. What data is irrelevant to solving this question?
- Movie start time at 7:45 (correct answer)
- Ticket price and number of tickets
- Popcorn price, coupon amount, and tax rate
- Candy price that he did not buy
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem involves movie purchases with coupons, taxes, and skipped or timed details. Choice A is correct because the movie start time at 7:45 is irrelevant to calculating the total cost. Choice D is incorrect because the skipped candy price is also irrelevant, but the question asks for irrelevant data, and A fits. To help students: Teach them to focus on purchased items and adjustments like coupons, while listing all data to spot irrelevancies. Watch for: students including times or skipped items in cost calculations.
Question 18
A train leaves at 9:10 a.m. and arrives at 11:05 a.m. After a 35-minute break, the next train arrives at 1:20 p.m. The traveler buys a snack at 10:00 a.m. The seat number is $14B$. How would you approach solving this problem?
- Add travel times and the break time; ignore snack and seat (correct answer)
- Use the snack time to estimate the first train's speed
- Subtract the break time from the first train's travel time
- Use seat number $14B$ to determine minutes traveled
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. To find total travel time, we need the first train's duration (9:10 a.m. to 11:05 a.m. = 1 hour 55 minutes), the break (35 minutes), and the second train's duration (11:05 a.m. + 35 minutes = 11:40 a.m. to 1:20 p.m. = 1 hour 40 minutes). Choice A is correct because it identifies adding these three time components while ignoring irrelevant details like snack time and seat number: 1:55 + 0:35 + 1:40 = 4 hours 10 minutes total. Choices B and D incorrectly suggest using snack time or seat number for calculations, while Choice C proposes subtracting break time which would give incorrect results. To help students: teach time arithmetic with careful attention to clock transitions, emphasize identifying start and end times for each segment, and practice recognizing when personal activities (snacks) don't affect scheduled times.
Question 19
A club sells 180 tickets at 6 each for a fundraiser. Renting the gym costs 250, and posters cost 40. They planned face painting for 35 but canceled it. The DJ volunteers for free. Which steps are necessary to find the fundraiser profit?
- Add all planned costs, including face painting, then subtract later
- Multiply tickets by price, then subtract gym and poster costs (correct answer)
- Subtract the DJ fee from ticket sales, then add costs
- Divide total costs by tickets sold to find profit per ticket
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. To find fundraiser profit, we need revenue (180 tickets × $6 = $1,080) minus actual costs (gym rental $250 + posters $40 = 290),ignoringthecanceledfacepaintingandfreeDJservice.ChoiceBiscorrectbecauseitidentifiesthepropersteps:multiplyticketsbypricetogetrevenue(1,080), then subtract the actual costs of gym rental and posters to find profit ($1,080 - $250 - $40 = $790). Choice A incorrectly includes the canceled face painting cost, Choice C unnecessarily mentions the DJ (which is free), and Choice D suggests an irrelevant calculation. To help students: emphasize distinguishing between planned versus actual expenses, teach them to identify revenue sources and actual costs separately, and practice recognizing when information about canceled or free items should be excluded from calculations. Question 20
A train ride is 1 hour 35 minutes, then there is a 25-minute transfer wait. The second train ride is 45 minutes. The station announces a 3 PM art show, and the ticket costs $6. How would you approach solving this problem?
- Add both ride times and the transfer wait time (correct answer)
- Subtract the art show time from the second ride
- Add the ticket cost to the travel minutes
- Use only the longer train ride time
Explanation: This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. In this scenario, the problem details train rides, transfers, and unrelated events like an art show and ticket costs. Choice A is correct because adding both ride times and the transfer wait time logically sequences the steps to find total travel time. Choice C is incorrect because it mixes ticket costs with travel minutes, a common error when students blend financial and temporal data. To help students: Teach them to categorize information by type, such as time versus cost, and practice summing durations in order. Watch for: students subtracting instead of adding times or including irrelevant announcements.