Unit Rate Comparisons - SHSAT Math

1. Computer A downloads 500 MB in 200 s. Computer B downloads 3 GB (3072 MB) in 900 s. Which computer has the faster download speed, and what is that speed in MB/s?
   Answer: Computer B, about $3.41$ MB/s When you see a question comparing rates, you need to calculate each rate separately and then compare them. Rate problems always follow the formula: rate = amount ÷ time. For Computer A: rate = 500 MB ÷ 200 s = 2.5 MB/s For Computer B: rate = 3072 MB ÷ 900 s ≈ 3.41 MB/s Since 3.41 > 2.5, Computer B has the faster download speed at approximately 3.41 MB/s. Looking at the wrong answers: Choice A correctly calculates Computer A's speed as 2.50 MB/s, but incorrectly identifies it as the faster computer. This is a trap for students who calculate both speeds but then compare them backwards. Choice C suggests both computers have the same speed of 2.95 MB/s, which might tempt students who try to average the two speeds instead of calculating them properly. Choice D claims the speeds can't be determined, which would only be true if we were missing essential information—but we have all the data needed (amount downloaded and time taken for each computer). The key trap here is in choice A: many students calculate correctly but then pick the wrong computer as "faster." Always double-check your comparison step. When comparing rates on the SHSAT, calculate each rate completely before deciding which is larger, and be extra careful about units—make sure you're comparing the same units (MB/s in this case).
2. Runner A finishes a 100-meter dash in 11.0 seconds. Runner B finishes a 200-meter race in 21.5 seconds. Which runner has the greater average speed, expressed in meters per second?
   Answer: Runner B, about $9.30$ m/s When you encounter speed problems, remember that average speed equals distance divided by time. This question tests whether you can calculate and compare speeds for different distances and times. To find each runner's average speed, divide their distance by their time. For Runner A: $\text{speed} = \frac{100 \text{ meters}}{11.0 \text{ seconds}} = 9.09 \text{ m/s}$. For Runner B: $\text{speed} = \frac{200 \text{ meters}}{21.5 \text{ seconds}} = 9.30 \text{ m/s}$. Runner B has the greater average speed. Choice A correctly calculates Runner A's speed but incorrectly concludes that Runner A is faster. This happens when you calculate accurately but forget to compare both results. Choice C suggests both runners have identical speeds of 9.20 m/s, which would only occur through an arithmetic error or by mistakenly averaging the two calculated speeds. Choice D claims you need more data, but speed calculations only require distance and time—both provided in the problem. The correct answer is B because Runner B's speed of 9.30 m/s exceeds Runner A's 9.09 m/s, despite Runner B running a longer distance that took more time. Strategy tip: On speed problems, always calculate both values completely before comparing. Don't assume the runner with the shorter time or distance is automatically faster—speed depends on the ratio of distance to time, not the individual components.
3. Grapes are sold in three bag sizes. 1.5 lb for $3.90 3 lb for $7.50 5 lb for $12.25 Which bag is the best buy based on price per pound?
   Answer: 5-lb bag at $2.45 per pound When you encounter unit rate problems like this, you need to find the cost per unit (price per pound) by dividing the total cost by the total weight for each option. Let's calculate the price per pound for each bag size: For the 1.5-lb bag: $\frac{\$3.90}{1.5 \text{ lb}} = \$2.60$ per pound For the 3-lb bag: $\frac{\$7.50}{3 \text{ lb}} = \$2.50$ per pound For the 5-lb bag: $\frac{\$12.25}{5 \text{ lb}} = \$2.45$ per pound The 5-lb bag has the lowest price per pound at $2.45, making it the best buy. Looking at the wrong answers: Choice A correctly calculates the unit rate for the 1.5-lb bag ($2.60 per pound) but this isn't the best deal since it's the highest price per pound. Choice B correctly calculates the 3-lb bag's rate ($2.50 per pound), but this is the middle option, not the best. Choice D claims all sizes cost the same, which is incorrect—the calculations clearly show different unit rates, and $2.52 isn't close to any of our calculated values. Notice that larger quantities often (but not always) offer better unit rates due to bulk pricing. Always calculate the unit rate rather than assuming—sometimes smaller sizes are actually better deals. When comparing unit rates, the lowest cost per unit gives you the most value for your money.
4. Club X raises $140 in 4 hours. Club Y raises $225 in 7 hours. Which club raises money at a higher rate, and what is that rate?
   Answer: Club X, $35 per hour When you see questions comparing rates, you need to calculate the rate for each situation and then compare them directly. A rate tells you how much something happens per unit of time. To find each club's fundraising rate, divide the total money raised by the time it took. For Club X: $\$140 ÷ 4 \text{ hours} = \$35$ per hour. For Club Y: $\$225 ÷ 7 \text{ hours} = \$32.14$ per hour (rounded). Since $\$35 > \$32.14$, Club X raises money at a higher rate. Looking at the wrong answers: Choice B correctly calculates Club Y's rate but incorrectly identifies it as the higher rate. This is a trap for students who calculate both rates but forget to compare them properly. Choice C suggests both clubs have the same rate of $33.60 per hour, which would only be true if you incorrectly averaged the two rates instead of calculating each one separately. Choice D claims the rates can't be compared, but since we have both the total amounts and time periods for each club, we have exactly the information needed to calculate and compare rates. The correct answer is A: Club X raises money at $35 per hour, which is higher than Club Y's rate. Strategy tip: On rate problems, always calculate each rate separately first, then compare. Don't be tempted to average rates or assume they're equal without doing the math. Write out your division clearly to avoid calculation errors.
5. Three cars travel the distances and use the fuel shown. • Car A: 360 mi on 12 gal • Car B: 300 mi on 10 gal • Car C: 430 mi on 14 gal Which car gets the best gas mileage in miles per gallon?
   Answer: Car C, about $30.7$ mpg When you encounter a gas mileage problem, you need to calculate miles per gallon (mpg) by dividing the distance traveled by the fuel consumed for each vehicle. Let's calculate the mpg for each car: Car A: $\frac{360 \text{ miles}}{12 \text{ gallons}} = 30$ mpg exactly Car B: $\frac{300 \text{ miles}}{10 \text{ gallons}} = 30$ mpg exactly Car C: $\frac{430 \text{ miles}}{14 \text{ gallons}} = 30.714...$ mpg, which rounds to about 30.7 mpg Since 30.7 mpg is higher than 30 mpg, Car C gets the best gas mileage. Choice A is incorrect because while Car A does get exactly 30 mpg, it doesn't have the best mileage among the three cars. Choice B is wrong for the same reason—Car B gets exactly 30 mpg but not the best. Choice D is incorrect because it claims all three cars have the same mileage at 30 mpg, but Car C actually gets about 30.7 mpg, which is better than the others. Choice C is correct because Car C gets approximately 30.7 mpg, which is the highest fuel efficiency of the three vehicles. Strategy tip: In comparison problems like this, always calculate the exact value for each option before determining which is best. Don't assume that similar-looking fractions will yield the same result—small differences in the numbers can lead to meaningfully different outcomes, as shown here where Car C's slightly better ratio makes it the clear winner.
6. Student M reads 90 pages in 150 minutes. Student N reads 60 pages in 100 minutes. Which statement is true about their reading rates?
   Answer: Both students read at the same rate of $36$ pages per hour When comparing rates, you need to calculate each person's speed in the same units to make a fair comparison. Reading rate problems test your ability to convert different time measurements and compute unit rates accurately. Let's find each student's reading rate in pages per hour. Student M reads 90 pages in 150 minutes. First, convert 150 minutes to hours: $150 ÷ 60 = 2.5$ hours. So Student M's rate is $90 ÷ 2.5 = 36$ pages per hour. Student N reads 60 pages in 100 minutes. Convert 100 minutes to hours: $100 ÷ 60 = \frac{5}{3}$ hours (or about 1.67 hours). Student N's rate is $60 ÷ \frac{5}{3} = 60 × \frac{3}{5} = 36$ pages per hour. Both students read at exactly 36 pages per hour, making answer choice C correct. Answer choice A incorrectly claims Student M reads faster, when both students read at the same rate. Answer choice B makes the same error for Student N. Answer choice D suggests the rates cannot be compared, but this is wrong—you can always compare rates when given complete information about pages read and time taken, regardless of knowing the total pages in their books. Remember this key strategy: when comparing rates with different time units, always convert to the same unit first (usually per hour for reading rates). Don't be fooled by different raw numbers—focus on the calculated rates per standard time unit.
7. A grocery store offers two different package sizes for trail mix. The small package contains 12 ounces for $4.80, while the large package contains 20 ounces for $7.60. If a customer wants to buy exactly 60 ounces of trail mix at the lowest possible cost, how much will they spend?
   Answer: $22.80 Find the unit price for each package. Small: $4.80 ÷ 12 = $0.40/ounce. Large: $7.60 ÷ 20 = $0.38/ounce. The large package is cheaper per ounce. To get exactly 60 ounces: 60 ÷ 20 = 3 large packages. Cost: 3 × $7.60 = $22.80. Choice B represents buying 2 large packages + 1 small package (52 oz) plus the need for more. Choice C assumes equal unit pricing. Choice D represents buying 5 small packages (60 oz) at $24.00.
8. Leak 1 drips 120 mL of water in 18 minutes. Leak 2 drips 180 mL in 24 minutes. Which leak has the slower drip rate, and what is that rate in mL per minute?
   Answer: Leak 1, about $6.67$ mL/min When you encounter rate problems, you need to calculate and compare unit rates by dividing the quantity by the time. This allows you to make fair comparisons even when the time periods differ. To find each leak's rate in mL per minute, divide the volume by the time: Leak 1: $\frac{120 \text{ mL}}{18 \text{ min}} = 6.67$ mL/min Leak 2: $\frac{180 \text{ mL}}{24 \text{ min}} = 7.50$ mL/min Since 6.67 < 7.50, Leak 1 has the slower drip rate at about 6.67 mL/min. Looking at the wrong answers: Choice B correctly calculates Leak 2's rate but incorrectly identifies it as the slower leak—7.50 mL/min is actually faster than Leak 1's rate. Choice C suggests both rates are equal at 7.00 mL/min, but this ignores the actual calculations showing different rates. Choice D claims the rates can't be compared because the times differ, but this reflects a fundamental misunderstanding—converting to unit rates (per minute) is exactly how we compare quantities measured over different time periods. Remember that unit rates are your tool for comparing any "per unit" quantities, whether it's speed (miles per hour), cost (dollars per pound), or efficiency (mL per minute). Always convert to the same unit of measurement, then compare the resulting numbers. The smaller rate indicates slower performance when dealing with quantities like dripping or leaking.
9. Three brands of floor tile are sold. Brand X: covers 20 sq ft for $9.80 Brand Y: covers 35 sq ft for $16.10 Brand Z: covers 50 sq ft for $23.75 Which brand has the lowest cost per square foot?
   Answer: Brand Y at $0.46 per sq ft When you encounter a problem comparing costs across different quantities, you need to find the unit rate—in this case, cost per square foot. This allows you to make a fair comparison between options with different coverage amounts. To find the cost per square foot for each brand, divide the total cost by the square footage covered: Brand X: $\frac{\$9.80}{20 \text{ sq ft}} = \$0.49$ per sq ft Brand Y: $\frac{\$16.10}{35 \text{ sq ft}} = \$0.46$ per sq ft Brand Z: $\frac{\$23.75}{50 \text{ sq ft}} = \$0.475 = \$0.48$ per sq ft (rounded) Brand Y has the lowest cost at $0.46 per square foot. Looking at the wrong answers: Choice A correctly calculates Brand X's unit rate but identifies it as the lowest when it's actually the highest at $0.49 per square foot. Choice C correctly calculates Brand Z's rate at $0.48 per square foot, but this is the middle value, not the lowest. Choice D claims all brands cost the same, which contradicts our calculations showing clear differences between the rates. When comparing unit rates on the SHSAT, always calculate each rate completely before deciding which is best. Don't assume that the option covering the most area or costing the most upfront will have the best or worst rate—you must do the division to know for certain.
10. Bus A has 48 seats and carries 36 passengers. Bus B has 56 seats and carries 40 passengers. Which bus has the higher occupancy rate (passengers per seat)?
    Answer: Bus A, occupancy $0.75$ When you encounter rate problems like this one, you're being asked to compare ratios by calculating each one separately. Occupancy rate means passengers per seat, so you need to divide the number of passengers by the number of seats for each bus. For Bus A: $\frac{36 \text{ passengers}}{48 \text{ seats}} = 0.75$ passengers per seat For Bus B: $\frac{40 \text{ passengers}}{56 \text{ seats}} = 0.714...$ passengers per seat, which rounds to $0.71$ Since $0.75 > 0.71$, Bus A has the higher occupancy rate. Looking at the answer choices: Choice A correctly identifies Bus A as having the higher occupancy rate and provides the accurate calculation of $0.75$. Choice B incorrectly claims Bus B has the higher rate, even though it does calculate Bus B's rate correctly as $0.71$. Choice C suggests the buses tie at $0.73$, but $0.73$ isn't the occupancy rate of either bus—this represents a calculation error, perhaps averaging the two rates instead of comparing them. Choice D claims we can't compare the data, but we have all the information needed: passenger counts and seat counts for both buses. Remember that rate problems require you to calculate each ratio individually before comparing. Don't be tempted to average values or assume you're missing information when all the necessary data is provided. Always double-check your division and compare the actual calculated values, not rounded approximations.
11. Factory Line P produces 120 parts in 45 minutes. Line Q produces 200 parts in 80 minutes. Which line has the greater production rate, in parts per hour?
    Answer: Line P, about $160$ parts per hour When you encounter rate problems, you need to convert all given information to the same units before comparing. Here, both production lines give data in different time periods, but the question asks for rates in parts per hour. To find each line's hourly production rate, convert the given rates to parts per hour. For Line P: $\frac{120 \text{ parts}}{45 \text{ minutes}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = \frac{120 \times 60}{45} = \frac{7200}{45} = 160$ parts per hour. For Line Q: $\frac{200 \text{ parts}}{80 \text{ minutes}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = \frac{200 \times 60}{80} = \frac{12000}{80} = 150$ parts per hour. Line P produces more parts per hour, so it has the greater production rate. Choice A correctly identifies Line P as having the greater rate at 160 parts per hour. Choice B incorrectly claims Line Q has the greater rate—while the calculation of 150 parts per hour for Line Q is correct, Line P's rate of 160 is higher. Choice C suggests both lines have equal rates of 155 parts per hour, which contradicts our calculations showing different rates of 160 and 150. Choice D claims the rates cannot be compared, but we have sufficient information to calculate and compare both rates. Always convert rates to common units before comparing them. Watch for answer choices that give correct calculations for individual parts but wrong overall conclusions about which is greater.
12. Recipe 1 uses 3 cups of flour to make 2 loaves of bread. Recipe 2 uses 7 cups of flour to make 5 loaves. Which recipe uses less flour per loaf?
    Answer: Recipe 2, $1.40$ cups per loaf When you encounter problems comparing rates or ratios, you need to find the unit rate for each option to make a fair comparison. Here, you're looking for cups of flour per loaf, so divide the total flour by the number of loaves for each recipe. For Recipe 1: $\frac{3 \text{ cups}}{2 \text{ loaves}} = 1.5$ cups per loaf For Recipe 2: $\frac{7 \text{ cups}}{5 \text{ loaves}} = 1.4$ cups per loaf Since $1.4 < 1.5$, Recipe 2 uses less flour per loaf. Looking at the answer choices: Choice A correctly calculates Recipe 1's rate but incorrectly claims it uses less flour per loaf. Choice B correctly identifies that Recipe 2 uses less flour and gives the right calculation of $1.40$ cups per loaf. Choice C suggests both recipes use the same amount of flour per loaf at $1.45$ cups, which appears to be an average of the two rates—but averaging doesn't make sense here since we're comparing which is less. Choice D claims we can't determine the answer, but we clearly have all the information needed to calculate both unit rates. Study tip: For rate comparison problems, always convert to the same unit (like "per loaf" or "per hour") before comparing. Watch out for answer choices that give you correct calculations but wrong conclusions about which is greater or less—read the question carefully to know what you're looking for.
13. Two printing machines work at different rates. Machine A prints 150 pages in 6 minutes, while Machine B prints 200 pages in 10 minutes. If both machines work simultaneously, how many complete pages will be printed in exactly 15 minutes?
    Answer: 675 pages Find each machine's rate per minute. Machine A: 150 ÷ 6 = 25 pages/minute. Machine B: 200 ÷ 10 = 20 pages/minute. Combined rate: 25 + 20 = 45 pages/minute. In 15 minutes: 45 × 15 = 675 pages. Choice B (650) results from incorrectly calculating Machine B's rate as 650÷15 backwards. Choice C (625) comes from using 25×25 instead of the combined rate. Choice D (600) results from using only Machine A's contribution over 15 minutes plus Machine B's contribution over 10 minutes.
14. A supermarket sells rice in two package sizes. A 5-pound bag costs $13.45, and a 2-pound bag costs $5.60. Which statement correctly compares the two unit prices?
    Answer: The 5-pound bag is cheaper, about $2.69 per pound. When you encounter unit price problems, you're looking to find the cost per single unit by dividing the total cost by the number of units. This lets you make fair comparisons between different package sizes. To find each unit price, divide the total cost by the weight. For the 5-pound bag: $\frac{\$13.45}{5 \text{ pounds}} = \$2.69$ per pound. For the 2-pound bag: $\frac{\$5.60}{2 \text{ pounds}} = \$2.80$ per pound. Since $\$2.69 < \$2.80$, the 5-pound bag offers the better deal at a lower price per pound. Looking at the wrong answers: Choice B incorrectly claims the 2-pound bag is cheaper and gives the wrong unit price ($2.80 is actually the correct unit price for the 2-pound bag, but it's more expensive, not cheaper). Choice C suggests both bags cost the same per pound at $2.75, which isn't true for either bag. Choice D claims there's insufficient information, but you have everything needed: total cost and weight for both packages. Choice A correctly identifies that the 5-pound bag is cheaper and provides the accurate unit price of $2.69 per pound. Study tip: Always calculate both unit prices completely before comparing. Don't assume larger packages are automatically better deals, and watch for answer choices that give correct calculations but wrong conclusions about which option is cheaper.
15. Car 1 travels 180 km in 2.25 h. Car 2 travels 155 km in 2.0 h. Which car has the greater average speed?
    Answer: Car 1 at $80$ km/h Speed problems require you to apply the fundamental formula: average speed = distance ÷ time. When comparing speeds, you need to calculate each one separately and then determine which is greater. For Car 1: average speed = $180 \text{ km} ÷ 2.25 \text{ h} = 80 \text{ km/h}$ For Car 2: average speed = $155 \text{ km} ÷ 2.0 \text{ h} = 77.5 \text{ km/h}$ Since $80 > 77.5$, Car 1 has the greater average speed at 80 km/h. Looking at the wrong answers: Answer B correctly calculates Car 2's speed as 77.5 km/h but incorrectly identifies it as the greater speed. This represents a comparison error after doing the math correctly. Answer C suggests both cars travel at 78.8 km/h, which appears to be an average of the two calculated speeds—a common mistake where students think they should find some kind of combined or middle value rather than comparing the individual speeds. Answer D claims the speeds cannot be compared, but this is false since we have all the necessary information (distance and time) for both cars to calculate and compare their average speeds. When you encounter speed comparison problems, always calculate each speed individually using the distance-time formula, then directly compare the numerical results. Don't look for shortcuts or try to combine the data in creative ways—the straightforward approach of "calculate, then compare" will reliably get you to the right answer.
16. A grocery sells single apples for $0.50 each, a bag of 6 apples for $2.70, and a bag of 12 apples for $5.10. Which purchase gives the lowest price per apple?
    Answer: Buying 12, at $0.425 per apple When you encounter pricing comparison problems, you need to calculate the unit price for each option to determine which offers the best value. This requires dividing the total cost by the number of items. Let's calculate the price per apple for each purchasing option. For single apples: $\$0.50 \div 1 = \$0.50$ per apple. For the 6-apple bag: $\$2.70 \div 6 = \$0.45$ per apple. For the 12-apple bag: $\$5.10 \div 12 = \$0.425$ per apple. The 12-apple bag gives you the lowest price per apple at $0.425, making option B correct. Looking at the wrong answers: Option A correctly calculates the unit price for 6 apples ($0.45) but incorrectly claims this is the lowest price. While $0.45 is lower than buying singles, it's still higher than the 12-apple option. Option C gives the correct unit price for singles ($0.50) but again incorrectly identifies this as the best deal—it's actually the most expensive option. Option D is completely false since the three options have distinctly different unit prices ($0.425, $0.45, and $0.50), and none of them equals $0.46. For unit price problems, always divide total cost by quantity for each option, then compare the results. Watch out for answer choices that give correct calculations but wrong conclusions—the SHSAT often includes these to test whether you can both calculate correctly and identify which result answers the actual question being asked.
17. Block P has a mass of 250 g and a volume of 200 cm³. Block Q has a mass of 400 g and a volume of 350 cm³. Block R has a mass of 330 g and a volume of 270 cm³. Which block has the greatest density in g/cm³?
    Answer: Block P at $1.25$ g/cm³ When you encounter density problems, remember that density is mass divided by volume ($\text{density} = \frac{\text{mass}}{\text{volume}}$). To find which block has the greatest density, you need to calculate the density for each block and compare the results. Let's calculate each density: Block P: $\frac{250 \text{ g}}{200 \text{ cm}^3} = 1.25 \text{ g/cm}^3$ Block Q: $\frac{400 \text{ g}}{350 \text{ cm}^3} = 1.143 \text{ g/cm}^3 \approx 1.14 \text{ g/cm}^3$ Block R: $\frac{330 \text{ g}}{270 \text{ cm}^3} = 1.222 \text{ g/cm}^3 \approx 1.22 \text{ g/cm}^3$ Block P has the highest density at 1.25 g/cm³, making choice A correct. Choice B incorrectly identifies Block Q as having the greatest density, but 1.14 g/cm³ is actually the lowest of the three. Choice C incorrectly identifies Block R as having the greatest density at 1.22 g/cm³, which is higher than Block Q but still less than Block P. Choice D incorrectly claims all blocks have the same density around 1.20 g/cm³—this might seem plausible since the values are relatively close, but the calculations clearly show different densities. On density problems, always calculate each value precisely rather than estimating. Small differences in density can be significant, and the SHSAT often includes answer choices that are close together to test your computational accuracy.
18. Two water pumps are filling a pool. Pump X fills the pool at a rate of 450 gallons in 18 minutes, while Pump Y fills at a rate of 320 gallons in 16 minutes. If the pool capacity is 1,800 gallons and Pump Y starts 6 minutes before Pump X, how much time will elapse from when Pump Y starts until the pool is completely full?
    Answer: 43 minutes 20 seconds Pump X's rate is 450 ÷ 18 = 25 gallons per minute, and Pump Y's rate is 320 ÷ 16 = 20 gallons per minute. During its 6-minute head start, Pump Y adds 6 × 20 = 120 gallons, leaving 1,800 − 120 = 1,680 gallons. Together the pumps add 25 + 20 = 45 gallons per minute, so they need 1,680 ÷ 45 = 37 1/3 minutes. The total time from when Pump Y starts is 6 + 37 1/3 = 43 1/3 minutes, which is 43 minutes 20 seconds. 46 minutes comes from having both pumps fill all 1,800 gallons (1,800 ÷ 45 = 40 minutes) and then adding the 6-minute head start, which counts Pump Y's first 120 gallons twice. 44 and 48 minutes are too long: after 44 minutes the pumps would already have moved 120 + 38 × 45 = 1,830 gallons.
19. A box of 18 identical pencils costs $4.50, a box of 50 costs $11.50, and a box of 30 costs $7.80. Which box offers the lowest price per pencil?
    Answer: The 50-pack at $0.23 per pencil When you encounter unit rate problems like this, you need to find the cost per individual item by dividing the total cost by the quantity. This allows you to make fair comparisons between different package sizes. Let's calculate the price per pencil for each box: For the 18-pack: $\frac{\$4.50}{18} = \$0.25$ per pencil For the 50-pack: $\frac{\$11.50}{50} = \$0.23$ per pencil For the 30-pack: $\frac{\$7.80}{30} = \$0.26$ per pencil The 50-pack offers the lowest price per pencil at $0.23, making choice B correct. Looking at the wrong answers: Choice A correctly calculates the 18-pack's unit price but incorrectly claims it's the lowest. Choice C accurately finds the 30-pack's unit price but also wrongly identifies it as the best deal. Choice D is completely incorrect—the prices per pencil clearly vary, and "$0.25" isn't even close to the actual range we calculated. Notice that the largest package doesn't automatically mean the best value, and you can't assume all options have the same unit price without doing the math. The question tests whether you can accurately perform division with decimals and compare the results. Strategy tip: On unit rate problems, always calculate each rate completely before comparing. Don't rely on估算 or assumptions about which package size offers the best deal—larger isn't always cheaper per unit.
20. Two printers produce flyers. Printer X makes 420 flyers in 7 minutes, and Printer Y makes 620 flyers in 10 minutes. Which printer works faster, and what is that rate?
    Answer: Printer Y, about 62 flyers per minute When you encounter rate problems, you need to find the unit rate by dividing the total amount by the total time. This lets you compare different scenarios on equal terms. To find each printer's rate, divide flyers by minutes: Printer X: $\frac{420 \text{ flyers}}{7 \text{ minutes}} = 60 \text{ flyers per minute}$ Printer Y: $\frac{620 \text{ flyers}}{10 \text{ minutes}} = 62 \text{ flyers per minute}$ Since 62 > 60, Printer Y works faster at 62 flyers per minute. This confirms answer choice B. Looking at the wrong answers: Choice A correctly calculates Printer X's rate as 60 flyers per minute, but incorrectly identifies it as the faster printer. Choice C claims both printers work at exactly 61 flyers per minute, which would require the rates to be equal—but our calculations show they're different (60 vs. 62). Choice D suggests we can't determine the faster printer, but we clearly can since we have all the necessary information to calculate both rates. Strategy tip: For SHSAT rate problems, always convert to the same unit before comparing. Calculate each rate separately, then compare the results. Watch out for answer choices that give you a correct calculation but pair it with the wrong conclusion—this is a common trap designed to catch students who do the math right but misread which value is larger.

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