- A bus leaves at 7:25 AM and arrives at 9:05 AM. After a 35-minute break, another bus ride takes 1 hour 10 minutes. The driver mentions a $3 coffee special at 8 AM. Which details are critical to finding the total travel time?
Answer: Departure and arrival times, break length, and second ride duration
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 bus rides, breaks, and an unrelated coffee special. Choice A is correct because departure and arrival times, break length, and second ride duration are critical for total travel time. Choice B is incorrect because the coffee special time and price do not affect travel, a common distraction from core timing. To help students: Teach them to timeline events, sum durations sequentially, and exclude promotional details. Watch for: students adding break times incorrectly or incorporating costs into time calculations.
- 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?
Answer: Add both ride times and the transfer wait time
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.
- 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?
Answer: Discount only the bricks, add soil, then add delivery fee
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.
- 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?
Answer: Discount the hoodie, add notebook, then apply 6% tax
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. - 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?
Answer: Ignore the hat, discount hoodie, add items, apply tax, use gift card
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) and a hoodie ($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), add the notebook and discounted hoodie ($12 + $15 = $27), apply 8% tax ($27 × 1.08 = $29.16), then subtract the gift card ($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.
- 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?
Answer: Add both flight durations and the layover duration
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.
- 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?
Answer: Boards used, nail buckets, and the $15 delivery fee
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 $4 each ($120), 2 nail buckets at $9 each ($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.
- A water tank is being filled by two pipes. Pipe A fills the tank at 15 gallons per minute, and Pipe B fills it at 25 gallons per minute. The tank has a leak that drains 8 gallons per minute. If the tank holds 480 gallons and is currently empty, which expression represents the time needed to fill it completely?
Answer: 15+25−8480 minutes
When you encounter rate problems involving multiple inputs and outputs, think about the net rate - the actual rate of change after considering all factors working together.
Here, you need to find how long it takes to fill a 480-gallon tank when two pipes are adding water while a leak is removing it. Pipe A adds 15 gallons per minute, Pipe B adds 25 gallons per minute, so together they add 15+25=40 gallons per minute. However, the leak removes 8 gallons per minute, so the net rate of filling is 40−8=32 gallons per minute.
Using the formula: Time = Total Amount ÷ Rate, you get 32480=15+25−8480 minutes, which is answer choice B.
Let's examine why the other choices are wrong. Choice A (15+25480) ignores the leak entirely - a common oversight that would overestimate the filling rate. Choice C ((15+25)×8480) incorrectly multiplies the input rate by the leak rate, creating a nonsensical calculation. Choice D (15+25480−8) subtracts the leak from the tank capacity rather than from the filling rate, which fundamentally misunderstands how rates work.
Strategy tip: In rate problems with multiple inputs and outputs, always calculate the net rate first by adding all inputs and subtracting all outputs. Then apply the standard Time = Amount ÷ Rate formula. Watch for answer choices that ignore one of the rates - this is a frequent trap. - 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?
Answer: Jacket and shirt prices, discount rate, and tax rate
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.
- A printing company charges $0.08 per page for the first 500 pages and $0.05 per page for each additional page. A school wants to print 1,200 pages and has a budget of $75. To determine if the budget is sufficient, what is the most efficient approach?
Answer: Calculate the cost for exactly 1,200 pages and compare to the budget
The question is whether $75 covers 1,200 pages, so the most direct check is to find the cost of exactly 1,200 pages and compare. The first 500 pages cost 500×0.08=40 dollars. The other 1,200−500=700 pages cost 700×0.05=35 dollars. The total is $40 + $35 = $75, which exactly matches the budget, so it is sufficient. Finding the most pages $75 can buy also reaches an answer, but it takes extra steps, since you must work backward through both price tiers, so calling both approaches equally efficient is not right. Calculating costs at several quantities wastes time on numbers nobody asked about. An average cost per page is not known in advance with two rates, so you would have to find the total first anyway. - 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?
Answer: The average speed including stop time
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.
- For a fundraiser car wash, the team washes 60 cars and charges $5 each. Soap and supplies cost $48, and they pay $30 for a sign. They also plan a raffle with 100 tickets, but it is postponed. What data is irrelevant to solving this question?
Answer: Raffle ticket plan that is postponed
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 car wash fundraiser with sales, costs, and a postponed plan. Choice C is correct because the raffle ticket plan that is postponed is irrelevant to current profit calculation. Choice A is incorrect because cars washed and price are essential, not irrelevant, a common mix-up in identifying unused data. To help students: Teach them to distinguish executed from planned actions, calculate actual revenues and costs, and verify irrelevance. Watch for: students including future plans or excluding key sales data.
- 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?
Answer: $50 + $35(3.5) + $20
The bill has three parts: $50 for the first hour, $35 for each hour after the first, and a flat $20 for materials. A 4.5-hour project has 4.5 - 1 = 3.5 hours after the first hour, so the total is $50 + $35(3.5) + $20, which works out to $50 + $122.50 + $20 = $192.50.
$50 + $35(4.5) + $20 charges the $35 rate for all 4.5 hours, so the first hour is paid for twice. $50 + $35(4) + $20 charges 4 additional hours instead of 3.5, as if the half hour were dropped rather than the first hour being subtracted. ($50 + $35)(4.5) + $20 applies both rates to every hour, and $35 + $50(3.5) + $20 swaps the two rates.
Study tip: In multi-rate problems, identify what triggers each rate. Only the first hour gets the $50 rate; every hour after it gets the $35 rate.
- 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 finding his total cost?
Answer: Movie start time at 7:45
To find Noah's total cost, list what he actually pays for. He buys 2 tickets at 11 dollars each, which is 22 dollars, and a 6-dollar popcorn. The coupon takes 3 dollars off the popcorn only, so the popcorn costs 6 − 3 = 3 dollars and the subtotal is 22 + 3 = 25 dollars. The 4% tax is then applied to that subtotal, so the total is 26 dollars. The movie start time of 7:45 tells when the movie begins, not what anything costs, so it is the irrelevant data. The ticket price and number of tickets are needed for the 22 dollars. The popcorn price, coupon and tax rate all change the total, and the tax rate cannot be skipped, because the final amount includes the 4% tax.
- 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?
Answer: Multiply tickets by price, then subtract gym and poster costs
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), ignoring the canceled face painting and free DJ service. Choice B is correct because it identifies the proper steps: multiply tickets by price to get revenue ($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.
- 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?
Answer: Book price, game price, discount rate, and tax rate
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.
- 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?
Answer: DJ music cost that was not used
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.
- 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?
Answer: First flight time, layover length, and second flight duration
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.
- A club sells 150 popcorn bags for $1.50 each. Each bag costs $0.60 to make, and they pay a $40 permit fee. The gym also hosts a free chess corner during the event. How would you approach solving this problem?
Answer: Find revenue, find total costs, then subtract to get profit
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 selling popcorn with costs and an unrelated free activity. Choice A is correct because finding revenue, total costs, then subtracting for profit logically sequences the solution. Choice C is incorrect because using the chess corner for extra income assumes unstated revenue, a common over-assumption. To help students: Teach them to compute revenue first, subtract all costs, and ignore free elements without financial impact. Watch for: students adding irrelevant activities or forgetting quantity in calculations.
- 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?
Answer: The planned talent show that was not held
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.
