SHSAT Math Quiz: Identifying Relevant Information
20 questions · exam conditions
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Identifying Relevant InformationQuestion 1 of 20

A clothing store is having a sale where customers receive different discounts based on their purchase amount. Purchases under $50 receive no discount. Purchases from $50 to $99.99 receive 15% off. Purchases from $100 to $199.99 receive 25% off. Purchases of $200 or more receive 35% off. Additionally, customers with a store membership card receive an extra 5% off their already discounted price. Sales tax of 8.5% is applied to the final discounted price.

A customer purchases items totaling $185 before any discounts and has a membership card. To calculate their final payment amount, which step must be completed before applying the membership discount?

Determine which discount tier applies to the $185 purchase amount
Calculate the sales tax on the original $185 purchase amount
Apply the 25% discount to find the first discounted price
Verify the customer's membership card status and eligibility
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SHSAT Math Quiz

SHSAT Math Quiz: Identifying Relevant Information

Practice Identifying Relevant Information in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Identifying Relevant Information, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

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.

All questions

Question 1

A clothing store is having a sale where customers receive different discounts based on their purchase amount. Purchases under $50 receive no discount. Purchases from $50 to $99.99 receive 15% off. Purchases from $100 to $199.99 receive 25% off. Purchases of $200 or more receive 35% off. Additionally, customers with a store membership card receive an extra 5% off their already discounted price. Sales tax of 8.5% is applied to the final discounted price.

A customer purchases items totaling $185 before any discounts and has a membership card. To calculate their final payment amount, which step must be completed before applying the membership discount?

  1. Determine which discount tier applies to the $185 purchase amount
  2. Calculate the sales tax on the original $185 purchase amount
  3. Apply the 25% discount to find the first discounted price (correct answer)
  4. Verify the customer's membership card status and eligibility
Explanation: The membership discount is applied to the 'already discounted price,' meaning the base discount must be calculated first. For $185, the 25% discount applies, giving a discounted price of $138.75. Then the 5% membership discount applies to $138.75, not the original $185. The sequence matters because the discounts are not simply additive.

Question 2

There are 423 graduates to be seated. Each row has 17 chairs, but 2 chairs in every row must remain empty for photographers. What is the minimum number of rows needed to seat all graduates?

  1. 25
  2. 28
  3. 29 (correct answer)
  4. 30
Explanation: This is a division problem with constraints that requires careful setup. When you see questions about seating arrangements or fitting items into containers with restrictions, you need to first determine the actual usable capacity per unit. Each row has 17 chairs total, but 2 must remain empty for photographers. This means each row can actually seat 17−2=1517 - 2 = 15 graduates. Now you need to find how many rows are required to seat all 423 graduates. Divide the total graduates by the usable seats per row: 423÷15=28.2423 ÷ 15 = 28.2. Since you can't have a fraction of a row, you must round up to the next whole number. You need 29 complete rows to ensure all 423 graduates have seats. Let's verify: 28 rows would seat 28×15=42028 × 15 = 420 graduates, leaving 3 graduates without seats. The 29th row provides space for those remaining graduates. Looking at the wrong answers: (A) 25 rows would only seat 25×15=37525 × 15 = 375 graduates, falling short by 48 people. (B) 28 rows seats exactly 420 graduates, but this leaves 3 graduates standing—the question asks for the minimum to seat ALL graduates. (D) 30 rows would work since 30×15=45030 × 15 = 450 seats, but this exceeds the minimum requirement. Study tip: In "minimum number needed" problems, always round up your division result when you get a decimal. The question is asking for the smallest whole number that satisfies the constraint—you can't partially fulfill the requirement.

Question 3

A bakery prepared 120 blueberry muffins, 150 chocolate-chip muffins, and 90 bran muffins for the morning rush. By noon, 65 blueberry muffins and 40 chocolate-chip muffins had been sold. The manager wants to package the remaining blueberry and chocolate-chip muffins into identical variety boxes that each contain exactly 3 blueberry muffins and 5 chocolate-chip muffins. What is the greatest number of complete boxes that can be made?

  1. 11
  2. 15
  3. 18 (correct answer)
  4. 22
Explanation: This is a constraint optimization problem where you need to find how many complete boxes can be made given specific ratios and limited ingredients. When you see questions about packaging items in fixed ratios, identify what limits your production. First, calculate the remaining muffins after sales. For blueberry: 120−65=55120 - 65 = 55 remaining. For chocolate-chip: 150−40=110150 - 40 = 110 remaining. Each box needs exactly 3 blueberry and 5 chocolate-chip muffins. To find the maximum boxes, determine which ingredient runs out first. From blueberry muffins: 55÷3=18.33...55 ÷ 3 = 18.33... boxes possible. From chocolate-chip muffins: 110÷5=22110 ÷ 5 = 22 boxes possible. Since you can only make complete boxes, the blueberry muffins limit you to 18 boxes. Verify: 18 boxes use 18×3=5418 × 3 = 54 blueberry muffins (leaving 1) and 18×5=9018 × 5 = 90 chocolate-chip muffins (leaving 20). Choice A (11) is too conservative—you have enough ingredients for more boxes. Choice B (15) doesn't fully utilize the available blueberry muffins. Choice D (22) represents what you could make if chocolate-chip muffins were the limiting factor, but this ignores that you'd need 22×3=6622 × 3 = 66 blueberry muffins when you only have 55. The answer is C (18). Remember: In ratio problems with multiple constraints, always calculate the maximum possible from each ingredient separately, then choose the smallest result—that's your limiting factor.

Question 4

A rectangular wall is 24 feet long and 10 feet high. Two rectangular windows, each 3 feet by 5 feet, and a door 4 feet by 7 feet will not be painted. One gallon of paint covers 350 square feet. How many whole gallons of paint are needed for one coat on the wall?

  1. 1 (correct answer)
  2. 2
  3. 3
  4. 4
Explanation: This is a classic area calculation problem that tests your ability to find the net area that needs to be painted by subtracting openings from the total wall area. Start by calculating the total wall area: 24 feet×10 feet=240 square feet24 \text{ feet} \times 10 \text{ feet} = 240 \text{ square feet} Next, find the total area that won't be painted. Each window is 3×5=15 square feet3 \times 5 = 15 \text{ square feet}, so two windows equal 2×15=30 square feet2 \times 15 = 30 \text{ square feet}. The door is 4×7=28 square feet4 \times 7 = 28 \text{ square feet}. Total unpainted area: 30+28=58 square feet30 + 28 = 58 \text{ square feet} The area needing paint is: 240−58=182 square feet240 - 58 = 182 \text{ square feet} Since one gallon covers 350 square feet and you only need to cover 182 square feet, less than one gallon is actually required. However, since the question asks for whole gallons needed, you must round up to 1 gallon. Looking at the wrong answers: Choice B (2 gallons) would be excessive since 2 gallons could cover 700 square feet. Choice C (3 gallons) and Choice D (4 gallons) are even more wasteful, covering 1,050 and 1,400 square feet respectively. These wrong answers likely trap students who make calculation errors or forget to subtract the openings from the total wall area. Strategy tip: In paint coverage problems, always subtract doors, windows, and other unpainted areas from the total surface area before dividing by the coverage per gallon. Remember to round up when asked for whole gallons.

Question 5

A novel contains 480 pages, including 16 pages of photographs that Jenna plans to skip. She read 54 pages on Monday and 73 pages on Tuesday. She wants to read the rest in equal whole-page amounts on Wednesday, Thursday, and Friday so she finishes Friday night. How many pages must she read each of those three days?

  1. 112
  2. 113 (correct answer)
  3. 117
  4. 118
Explanation: When you encounter multi-step word problems like this, break down the information systematically and identify what you're solving for. This question tests your ability to organize given information and work through sequential calculations. First, determine how many pages Jenna actually needs to read. The novel has 480 pages total, but she's skipping 16 pages of photographs, so she needs to read 480−16=464480 - 16 = 464 pages. Next, calculate how many pages she's already read. Monday: 54 pages, Tuesday: 73 pages. Total read so far: 54+73=12754 + 73 = 127 pages. Now find how many pages remain: 464−127=337464 - 127 = 337 pages left to read over three days (Wednesday, Thursday, and Friday). Since she wants to read equal amounts each day, divide the remaining pages by 3: 337÷3=112.33...337 ÷ 3 = 112.33... pages per day. Since she must read whole pages, round up to 113 pages per day. Let's verify: 113×3=339113 × 3 = 339 pages, which is slightly more than the 337 needed, but this ensures she finishes by Friday night. Choice A (112) falls short because 112×3=336112 × 3 = 336 pages, leaving 1 page unfinished. Choice C (117) means 117×3=351117 × 3 = 351 pages, which is unnecessarily high. Choice D (118) gives 118×3=354118 × 3 = 354 pages, also too many. The answer is B (113). Strategy tip: In division problems requiring whole numbers, pay attention to whether you need to round up or down based on the real-world context. Here, rounding up ensures completion of the task.

Question 6

A cylindrical tank holds 380 gallons when full. Water flows in at 12 gallons per minute. When the tank is half full, a drain opens and removes water at 7 gallons per minute while the filling continues. How many minutes after filling begins will the tank first become completely full?

  1. 32 minutes
  2. 46 minutes
  3. 54 minutes (correct answer)
  4. 68 minutes
Explanation: When you encounter multi-stage filling problems, break them into distinct phases where conditions change. This problem has two phases: filling alone, then filling with simultaneous draining. Phase 1: The tank fills from empty to half-full (190 gallons) at 12 gallons per minute. Time needed: 190÷12=1556190 ÷ 12 = 15\frac{5}{6} minutes. Phase 2: At the half-full mark, the drain opens while filling continues. Now you have a net rate: 12 gallons in minus 7 gallons out = 5 gallons per minute net inflow. The tank needs another 190 gallons to reach full capacity. Time needed: 190÷5=38190 ÷ 5 = 38 minutes. Total time: 1556+38=535615\frac{5}{6} + 38 = 53\frac{5}{6} minutes, which rounds to 54 minutes, making C correct. Choice A (32 minutes) likely comes from calculating only the second phase (38 minutes) but making an error in the net rate calculation. Choice B (46 minutes) might result from incorrectly assuming the drain rate changes the problem dynamics or miscalculating the half-full point. Choice D (68 minutes) could come from adding the drain rate instead of subtracting it, giving 12 + 7 = 19 gallons per minute in the second phase. Study tip: In rate problems with changing conditions, always identify when conditions change, calculate each phase separately, then combine the times. Watch out for net rate calculations—when flows oppose each other, subtract the rates.

Question 7

A school is taking 196 students on a field trip. Identical buses will be hired, and no bus may carry more than 52 passengers. Because of safety rules, 2 seats on each bus must be left empty for chaperones who will ride in separate cars. What is the minimum number of buses the school must hire?

  1. 3
  2. 4 (correct answer)
  3. 5
  4. 6
Explanation: This is a word problem involving division with constraints, which requires you to think about real-world limitations rather than just performing straight division. First, determine how many students each bus can actually carry. While buses hold 52 passengers maximum, 2 seats must remain empty for chaperones, so each bus can carry 52−2=5052 - 2 = 50 students. Now divide the total students by the capacity per bus: 196÷50=3.92196 ÷ 50 = 3.92. Since you can't hire a fraction of a bus, you must round up to 4 buses. Let's verify: 3 buses carry 3×50=1503 × 50 = 150 students, leaving 46 students without transportation. The fourth bus will carry these remaining 46 students (well within the 50-student capacity). Looking at the wrong answers: Choice (A) 3 buses represents the trap of rounding down instead of up—3 buses only transport 150 students, leaving 46 stranded. Choice (C) 5 buses occurs if you mistakenly divide 196 by 40 instead of 50, perhaps confusing how the chaperone seats work. Choice (D) 6 buses suggests dividing by an even smaller capacity, showing a misunderstanding of the constraint. The correct answer is (B) 4 buses. Remember: In real-world division problems, always consider what the remainder means practically. When you need to transport people, serve customers, or fill containers, you typically must round up to ensure everyone or everything is accommodated. Don't automatically round down just because it's mathematically smaller.

Question 8

A farmer loaded 16 crates of apples onto a truck. Twelve crates weighed 42 lb each, and the other four weighed 38 lb each. The empty truck weighs 4,500 lb, and the maximum legal loaded weight is 5,200 lb. How many additional 50-lb bags of potatoes can be loaded without exceeding the limit?

  1. 0 (correct answer)
  2. 1
  3. 2
  4. 3
Explanation: When you encounter weight limit problems, you need to track current weight and compare it to the maximum capacity to find remaining space. Let's calculate the truck's current weight. The 12 heavy crates weigh 12×42=50412 \times 42 = 504 pounds, and the 4 lighter crates weigh 4×38=1524 \times 38 = 152 pounds. Adding the empty truck weight: 4,500+504+152=5,1564,500 + 504 + 152 = 5,156 pounds currently loaded. With a maximum legal weight of 5,200 pounds, the remaining capacity is 5,200−5,156=445,200 - 5,156 = 44 pounds. Since each potato bag weighs 50 pounds, and 50 > 44, you cannot add even one bag without exceeding the limit. Looking at the wrong answers: Choice B (1 bag) would create a total weight of 5,156+50=5,2065,156 + 50 = 5,206 pounds, which exceeds the 5,200-pound limit by 6 pounds. Choice C (2 bags) would add 100 pounds, reaching 5,256 pounds—56 pounds over the limit. Choice D (3 bags) would add 150 pounds, reaching 5,306 pounds—106 pounds over the limit. All of these violate the legal weight restriction. The answer is A: 0 bags can be added safely. Strategy tip: In weight limit problems, always calculate the exact remaining capacity first, then see how many complete units fit within that space. Don't assume you can add "most of" a unit—on the SHSAT, you typically need whole numbers of items, and safety regulations require staying under the limit, not meeting it exactly.

Question 9

A pizzeria cuts each large pizza into 12 slices and each medium pizza into 8 slices. For a party, the manager orders 10 large pizzas and just enough medium pizzas so the total number of slices is exactly 200. How many medium pizzas did she order?

  1. 5
  2. 8
  3. 10 (correct answer)
  4. 12
Explanation: This is a linear equation problem where you need to set up an equation with one unknown variable. When you see word problems involving totals and different rates or sizes, think about identifying what you know versus what you need to find. Start by organizing the given information: large pizzas have 12 slices each, medium pizzas have 8 slices each, there are 10 large pizzas, and the total slices must equal 200. Let's call the number of medium pizzas mm. The total slices equation becomes: 10×12+m×8=20010 \times 12 + m \times 8 = 200 Simplifying: 120+8m=200120 + 8m = 200 Subtract 120 from both sides: 8m=808m = 80 Divide by 8: m=10m = 10 So 10 medium pizzas were ordered, making C correct. Let's check why the other answers don't work. Choice A (5 medium pizzas) would give us 120+5×8=160120 + 5 \times 8 = 160 total slices, which is 40 slices short. Choice B (8 medium pizzas) would give us 120+8×8=184120 + 8 \times 8 = 184 total slices, still 16 slices short. Choice D (12 medium pizzas) would give us 120+12×8=216120 + 12 \times 8 = 216 total slices, which exceeds the target by 16 slices. When solving word problems like this, always define your variable clearly, set up the equation systematically, and verify your answer by substituting back into the original problem. The key is translating the words into mathematical relationships accurately.

Question 10

A cookie recipe that makes 30 cookies needs 2.5 cups flour, 1.75 cups sugar, and 1 cup butter. Helen wants to bake 72 cookies. She has 5 cups flour, 4 cups sugar, and 3 cups butter. Which ingredient will she run out of first?

  1. Flour (correct answer)
  2. Sugar
  3. Butter
  4. None—she has enough of all three
Explanation: This problem tests proportional reasoning and resource constraints. When scaling recipes, you need to determine how much of each ingredient is required, then check what limits your production. First, find the scaling factor. Helen wants 72 cookies from a recipe that makes 30: 7230=2.4\frac{72}{30} = 2.4. So she needs 2.4 times the original amounts. Calculate the required ingredients:
  • Flour: 2.5×2.4=62.5 \times 2.4 = 6 cups
  • Sugar: 1.75×2.4=4.21.75 \times 2.4 = 4.2 cups
  • Butter: 1×2.4=2.41 \times 2.4 = 2.4 cups
Now compare what she needs versus what she has:
  • Flour: needs 6 cups, has 5 cups (short by 1 cup)
  • Sugar: needs 4.2 cups, has 4 cups (short by 0.2 cups)
  • Butter: needs 2.4 cups, has 3 cups (has enough)
Since Helen is short on both flour and sugar, determine which runs out first by finding how many cookies each ingredient can actually make. Her 5 cups of flour can make 52.5×30=60\frac{5}{2.5} \times 30 = 60 cookies. Her 4 cups of sugar can make 41.75×30≈68.6\frac{4}{1.75} \times 30 ≈ 68.6 cookies. Choice A is correct—flour limits her to only 60 cookies. Choice B is wrong because sugar allows more cookies than flour does. Choice C is wrong because she has plenty of butter. Choice D is wrong because she's short on two ingredients. Strategy tip: In scaling problems, always identify the "limiting reagent"—the ingredient that runs out first determines your maximum output.

Question 11

A car gets 30 miles per gallon on the highway and about 26.7 miles per gallon in the city. The driver plans a 450-mile trip with 60% of the distance on the highway. About how many gallons of gas should the driver expect to use?

  1. 14 gal
  2. 15 gal
  3. 16 gal (correct answer)
  4. 18 gal
Explanation: This is a fuel efficiency problem that requires you to handle different rates for different portions of a trip. When you see mixed conditions like highway and city driving, calculate the fuel needed for each segment separately, then add them together. First, find the distance for each type of driving. With 60% highway driving: highway distance = 0.60×450=2700.60 \times 450 = 270 miles, and city distance = 450−270=180450 - 270 = 180 miles. Next, calculate gallons needed for each segment using the formula: gallons = distance ÷ miles per gallon. For highway driving: 270÷30=9270 \div 30 = 9 gallons. For city driving: 180÷26.7≈6.74180 \div 26.7 ≈ 6.74 gallons. Total gallons needed: 9+6.74=15.749 + 6.74 = 15.74 gallons, which rounds to about 16 gallons. Looking at the wrong answers: Choice A (14 gal) likely comes from using only the highway rate for the entire trip (450÷30=15450 \div 30 = 15, then rounding down). Choice B (15 gal) might result from calculation errors in the city portion or premature rounding. Choice D (18 gal) could come from using only the city rate for the whole trip (450÷26.7≈16.9450 \div 26.7 ≈ 16.9, rounded up) or from computational mistakes. The correct answer is C (16 gal). Strategy tip: For mixed-rate problems, always break the trip into segments and calculate each separately. Don't try to find an "average" rate first—it's more error-prone and time-consuming than the segment approach.

Question 12

Refer to the table to answer the question. What was the average number of cups of lemonade sold per day in June?

  1. 29
  2. 31
  3. 34 (correct answer)
  4. 36
Explanation: June sales: 748 cups over 22 days → 748 ÷ 22 = 34 cups per day.
A/B/D: Division errors or wrong month selected.

Question 13

A delivery truck travels from warehouse A to store B, then to store C, and finally back to warehouse A. The distance from A to B is 18 miles, from B to C is 25 miles, and from C back to A is 31 miles. The truck averages 22 miles per gallon and gas costs $3.20 per gallon. The driver earns $18 per hour and the trip takes 3.5 hours total. The truck also has a maintenance cost of $0.15 per mile driven. To find the total cost per mile for this delivery route, which approach would be most efficient?

  1. Calculate fuel costs first, then add hourly wages and maintenance costs separately
  2. Find the total distance traveled, then calculate all costs and divide by distance (correct answer)
  3. Determine the cost for each leg of the trip individually, then average them
  4. Calculate time-based costs and distance-based costs as separate categories
Explanation: To find cost per mile, we need total cost divided by total distance. The most efficient approach is to find total distance (18 + 25 + 31 = 74 miles), calculate total costs (fuel + wages + maintenance), then divide. This avoids redundant calculations and directly gives the desired metric.

Question 14

A bakery produces three types of cookies: chocolate chip, oatmeal, and sugar cookies. On Monday, they made 240 chocolate chip cookies, 180 oatmeal cookies, and 300 sugar cookies. Each chocolate chip cookie uses 3 chocolate chips and costs $0.45 in ingredients. Each oatmeal cookie uses 2 tablespoons of oats and costs $0.30 in ingredients. Each sugar cookie uses 1 tablespoon of sugar and costs $0.25 in ingredients. The bakery sells chocolate chip cookies for $1.25 each, oatmeal cookies for $1.00 each, and sugar cookies for $0.85 each.

To determine which type of cookie generates the highest profit margin percentage, which information would be most relevant to identify first?

  1. The total number of each type of cookie produced on Monday
  2. The specific ingredients and quantities used in each cookie type
  3. The ingredient cost and selling price for each type of cookie (correct answer)
  4. The total revenue generated from all cookie sales combined
Explanation: Profit margin percentage is calculated as (selling price - cost) ÷ selling price × 100%. To find this, we need the ingredient cost and selling price for each cookie type. The production quantities and specific ingredient amounts are not needed for margin calculations, and total revenue doesn't help compare individual margins.

Question 15

A water tank is being filled by two pipes simultaneously. Pipe A fills the tank at a rate of 15 gallons per minute, while Pipe B fills it at 12 gallons per minute. However, Pipe A only operates for 20 minutes out of every hour due to an automatic timer. Pipe B runs continuously. The tank has a capacity of 1,800 gallons and currently contains 450 gallons. There is also a small leak that drains 2 gallons per minute continuously.

To find when the tank will be completely full, which factor creates the most complexity in the solution strategy?

  1. The continuous leak that reduces the effective fill rate throughout
  2. The initial amount of water already present in the tank
  3. The different flow rates between Pipe A and Pipe B systems
  4. The timer system that makes Pipe A operate intermittently rather than continuously (correct answer)
Explanation: When you encounter complex rate problems with multiple variables, look for which factor makes the problem hardest to solve systematically. This question tests your ability to identify what creates the greatest computational complexity. The timer system that makes Pipe A operate intermittently (answer D) creates the most complexity because it forces you to break the problem into repeating cycles. You can't simply calculate a constant combined rate and divide. Instead, you must track what happens during each 60-minute period: for 20 minutes, both pipes work (giving you 15 + 12 - 2 = 25 gallons per minute net), then for 40 minutes, only Pipe B works (giving you 12 - 2 = 10 gallons per minute net). This creates a repeating pattern that requires careful tracking of time intervals and accumulated water. Answer A is wrong because the continuous leak simply reduces the effective rate by a constant 2 gallons per minute throughout—this is straightforward to incorporate. Answer B is incorrect because the initial 450 gallons just changes your target from filling 1,800 gallons to filling the remaining 1,350 gallons—a simple subtraction. Answer C misses the point because different flow rates alone don't create complexity; you'd just add them together if both ran continuously. For SHSAT rate problems, watch for intermittent operations or changing conditions over time. These force you to break problems into phases rather than using simple rate equations, significantly increasing the complexity of your solution strategy.

Question 16

A school cafeteria serves lunch to 450 students daily. They offer three lunch options: pizza at $3.50, salad at $4.25, and sandwich combo at $5.00. Historical data shows that 40% of students choose pizza, 25% choose salad, and 35% choose the sandwich combo. The cafeteria wants to increase total daily revenue by $200. They are considering either raising all prices by the same percentage or changing the proportions of students who choose each option through better marketing.

To evaluate whether a uniform price increase or a marketing strategy would be more effective, which calculation should be prioritized?

  1. The current total daily revenue generated by all lunch sales (correct answer)
  2. The percentage price increase needed to achieve the $200 revenue goal
  3. The specific changes in customer choice percentages required for the marketing approach
  4. The profit margin difference between the three lunch options offered
Explanation: Before comparing strategies, we need the baseline: current daily revenue = 450 × (0.40 × $3.50 + 0.25 × $4.25 + 0.35 × $5.00). This establishes the foundation for calculating both the percentage increase needed and the magnitude of changes required in customer preferences. Without this baseline, we cannot evaluate which approach is more realistic or effective.

Question 17

A gardener is planning a rectangular vegetable garden. She wants the length to be 4 feet longer than twice the width. The garden must have an area of at least 150 square feet but no more than 300 square feet due to space constraints. Fencing costs $8 per linear foot, and she has a budget of $200 for fencing. The gardener also needs to leave a 2-foot border around the entire garden that cannot be planted.

Which constraint should be checked first to determine if the garden plan is feasible?

  1. Whether the area falls within the 150-300 square foot range
  2. Whether the fencing cost stays within the $200 budget limit (correct answer)
  3. Whether the border requirement affects the plantable area significantly
  4. Whether the length-to-width ratio creates a practical garden shape
Explanation: The fencing budget creates the most restrictive constraint. With the relationship L = 2W + 4, the perimeter is 6W + 8. For this to cost ≤ $200, we need 6W + 8 ≤ 25, so W ≤ 2.83 feet. This severely limits possible dimensions and should be checked first, as it may eliminate the feasibility before considering other constraints.

Question 18

A rectangular swimming pool is being filled with water. The pool has a length of 30 feet, a width of 20 feet, and a depth of 6 feet. Water flows into the pool at a rate of 45 gallons per minute. There are 7.48 gallons in one cubic foot. The pool also has a drain that removes water at 8 gallons per minute when open. The pool currently contains 1,200 gallons of water.

To find how long it takes to fill the pool completely with the drain closed, which piece of information is sufficient but NOT necessary?

  1. The rate at which the drain removes water from the pool (correct answer)
  2. The conversion factor between cubic feet and gallons of water
  3. The current amount of water already in the pool
  4. The dimensions of length, width, and depth of the pool
Explanation: Since the problem states the drain is closed, the drain rate (8 gallons per minute) is not needed. We need the pool dimensions to calculate total volume, the conversion factor to convert to gallons, the current water amount to find remaining capacity, and the fill rate. The drain rate is given but irrelevant when the drain is closed.

Question 19

An art teacher needs at least 180 markers. Packs of 24 markers cost $7, and packs of 12 markers cost $4. If she decides to buy exactly five 24-packs, what is the minimum number of 12-packs she must also buy?

  1. 4
  2. 5 (correct answer)
  3. 6
  4. 7
Explanation: This is an optimization problem where you need to find the minimum additional purchase to meet a requirement. When you see "at least" combined with "minimum number," you're looking for the smallest value that satisfies the constraint. Start by calculating what five 24-packs provide: 5×24=1205 \times 24 = 120 markers. Since the teacher needs at least 180 markers, she still needs 180−120=60180 - 120 = 60 more markers. Now determine how many 12-packs are needed to get at least 60 markers. Each 12-pack contains 12 markers, so you need 6012=5\frac{60}{12} = 5 packs exactly. Let's verify: 5×12=605 \times 12 = 60 markers, which gives her exactly 120+60=180120 + 60 = 180 total markers, meeting the "at least 180" requirement. Looking at the wrong answers: Choice A (4 packs) would give only 4×12=484 \times 12 = 48 additional markers, totaling 120+48=168120 + 48 = 168 markers, which falls short of the 180 requirement. Choice C (6 packs) would provide 6×12=726 \times 12 = 72 additional markers for 192 total markers, which exceeds the requirement but isn't the minimum needed. Choice D (7 packs) gives even more excess markers at 204 total, making it unnecessarily expensive. The key insight is that "at least" means you need to meet or exceed the target, but "minimum number" means you want the smallest quantity that accomplishes this. Always calculate the exact shortage first, then find the smallest whole number of items that covers that shortage.

Question 20

Students spent $48 on ingredients and baked 200 cookies for a fundraiser. They sold the cookies for $0.75 each and donated any unsold cookies. If they made a $72 profit, how many cookies were not sold?

  1. 20
  2. 32
  3. 40 (correct answer)
  4. 48
Explanation: This is a profit and loss problem that requires you to work backwards from the given information. When you see questions involving costs, revenue, and profit, remember that Profit = Revenue - Costs. Let's set up what we know: The students spent $48 on ingredients and made a $72 profit. Since Profit = Revenue - Costs, their total revenue must be $\72 + $48 = $120 . They sold cookies at 0.75 each, so the number of cookies sold = $$\120 ÷ $0.75 = 160$$ cookies. Since they baked 200 cookies total and sold 160, the number of cookies not sold = 200−160=40200 - 160 = 40 cookies. Looking at the wrong answers: Choice A (20) would mean they sold 180 cookies, generating 180×$0.75=$135180 × \$0.75 = \$135 in revenue and $135−$48=$87\$135 - \$48 = \$87 profit—too high. Choice B (32) would mean 168 cookies sold, generating 168×$0.75=$126168 × \$0.75 = \$126 revenue and $126−$48=$78\$126 - \$48 = \$78 profit—still too high. Choice D (48) would mean 152 cookies sold, generating 152×$0.75=$114152 × \$0.75 = \$114 revenue and $114−$48=$66\$114 - \$48 = \$66 profit—too low. Only choice C gives the correct $72 profit. Study tip: In profit problems, always identify all three components (costs, revenue, profit) and use the relationship Profit = Revenue - Costs to find the missing piece. Work systematically through the given information rather than jumping to calculations.