Identifying Relevant Information
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SSAT Middle Level: Quantitative › Identifying Relevant Information
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?
Use seat number $14B$ to determine minutes traveled
Subtract the break time from the first train’s travel time
Add travel times and the break time; ignore snack and seat
Use the snack time to estimate the first train’s speed
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.
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?
Ignore the hat, discount hoodie, add items, apply tax, use gift card
Use the hat price to estimate, then add the gift card value
Add the original prices, then subtract $25%$ at the end
Apply tax first, then take $25%$ off the taxed total
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) 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.
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 flyer cost and number of flyers printed
The number of cupcakes and price per cupcake
The ingredient cost and the table rental cost
The planned talent show that was not held
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.
A class buys $4$ science kits at $\$18$ each and gets $15%$ off the kits. Shipping is $$12$, and tax is $5%$ on the discounted kits only. A different kit costs $\$25$ but is out of stock. The teacher brings $10$ markers from home. Which details are critical to finding the answer?
Kit count and price, discount rate, shipping, and tax rule
Out-of-stock kit price and number of markers brought
Only the $5%$ tax rate and the $\$12$ shipping fee
Add shipping to kits first, then take $15%$ off everything
Explanation
This question tests middle school problem-solving skills, specifically identifying relevant information and planning a solution path in word problems. This skill involves discerning necessary details from extraneous data and logically sequencing steps to solve problems, crucial for real-world applications. The class's total cost requires: kit cost (4 × $18 = $72), apply 15% discount to kits ($72 × 0.85 = $61.20), add shipping ($12), apply 5% tax to discounted kits only ($61.20 × 0.05 = $3.06), for a total of $61.20 + $12 + $3.06 = $76.26. Choice B is correct because it identifies all critical components: kit count and price for the base cost, discount rate for savings, shipping as an additional cost, and the tax rule specifying tax applies only to discounted kits. Choice A incorrectly includes irrelevant information about out-of-stock items and markers, Choice C omits crucial kit information, and Choice D suggests an incorrect calculation sequence. To help students: teach careful reading of tax and discount applications, emphasize identifying what's actually purchased versus mentioned, and practice multi-step problems with conditional rules.
Leah buys $3$ pens at $\$2$ each and a binder for $$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?
Round all prices to the nearest $\$10$ for easier math
Apply $6%$ tax to $\$8$ before using the coupon
Ignore the notebook and find the binder’s discounted price
Add the notebook price to make the total more accurate
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), a binder ($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.
A patio is being built using $48$ square tiles, each costing $\$1.25$. Workers also need $3$ bags of grout at $$7$ each. A sealant costs $\$10$ but is not used. The job takes $2$ days. Which steps are necessary to find the total cost of materials?
Add $2$ days to the cost because time always adds expense
Multiply tile cost, add grout cost, and ignore the unused sealant
Divide total tiles by grout bags to find the cost per day
Include sealant cost, then subtract it after finding the total
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 patio material cost includes only tiles (48 × $1.25 = $60) and grout (3 × $7 = $21), totaling $81 - the unused sealant and work duration are irrelevant to material costs. Choice A is correct because it properly identifies multiplying tile quantity by price, adding grout cost, and ignoring the unused sealant - exactly the steps needed for accurate calculation. Choice B incorrectly suggests adding time to cost, Choice C unnecessarily includes then subtracts the unused sealant, and Choice D proposes an illogical calculation mixing unrelated quantities. To help students: teach them to distinguish between material costs and labor time, emphasize reading for what's actually used versus available, and practice identifying cost categories in construction problems to avoid mixing different types of information.
Maya flies from City A to City B in $2$ hours $15$ minutes. Her layover is $55$ minutes, then the next flight is $1$ hour $40$ minutes. She eats lunch for $30$ minutes during the layover. The airport gate number is $C12$. Which details are critical to finding the total travel time?
Gate number and first flight time only
First flight time, layover length, and second flight time
Subtract lunch time from the second flight time
Lunch time and gate number during the layover
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. Maya's total travel time requires adding the first flight (2 hours 15 minutes), the layover (55 minutes), and the second flight (1 hour 40 minutes) - the lunch time during layover and gate number are irrelevant details. Choice A is correct because it identifies exactly these three critical time components needed to calculate total travel time: first flight + layover + second flight = 2:15 + 0:55 + 1:40 = 4 hours 50 minutes. Choices B and C incorrectly include irrelevant details like lunch time and gate number, while Choice D suggests an illogical operation of subtracting lunch from flight time. To help students: teach them to focus on what the question asks (total travel time), identify all time-related information, and recognize that activities during waiting periods don't extend the scheduled times. Watch for students who confuse concurrent activities (lunch during layover) with sequential time additions.
On a shopping trip, Kai buys a $\$30$ jacket and a $$10$ scarf. The jacket has $20%$ off, and there is $7%$ sales tax on the discounted total. Socks cost $\$6$ and a hat costs $$12$, but neither is purchased. Kai also earns $15$ reward points. What information do you need to solve this problem?
Only the $7%$ tax rate and the jacket’s original price
Prices of jacket and scarf, discount rate, and tax rate
Reward points and the scarf color to choose the right tax
Prices of socks and hat, plus the $15$ reward points
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 calculate Kai's total cost: jacket with 20% off ($30 × 0.80 = $24), add scarf ($10), giving subtotal of $34, then apply 7% tax ($34 × 1.07 = $36.38) - unpurchased items and reward points are irrelevant. Choice A is correct because it identifies exactly the necessary information: prices of purchased items (jacket and scarf), the discount rate for the jacket, and the tax rate applied to the discounted total. Choices B and D incorrectly include irrelevant details like unpurchased items, reward points, or scarf color, while Choice C omits the crucial scarf price. To help students: teach them to first identify what's actually purchased, then apply discounts and taxes in the correct order, and practice recognizing when loyalty programs or product details don't affect the current transaction's cost.
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
Divide total costs by tickets sold to find profit per ticket
Subtract the DJ fee from ticket sales, then add costs
Multiply tickets by price, then subtract gym and poster costs
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), 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.
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?
Use only the $\$6$ boards because they cost more
Boards used, nail buckets, and the $\$15$ delivery fee
Include the $3$ hours to convert time into dollars
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 $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.