HSPT Quantitative Quiz: Apply Quantitative Logic
20 questions · exam conditions
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Apply Quantitative LogicQuestion 1 of 20

Of 30 swimmers, 18 swim freestyle, 14 swim backstroke, and 6 swim both. How many swim neither?

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HSPT Quantitative Quiz

HSPT Quantitative Quiz: Apply Quantitative Logic

Practice Apply Quantitative Logic in HSPT Quantitative 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 Apply Quantitative Logic, giving you a quick way to practice the rules, question types, and explanations that matter most for HSPT Quantitative.

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

Of 30 swimmers, 18 swim freestyle, 14 swim backstroke, and 6 swim both. How many swim neither?

  1. 2
  2. 4 (correct answer)
  3. 6
  4. 8
Explanation: Add the swimmers in each stroke: 18 + 14 = 32. The 6 who swim both were counted twice, so subtract them: 32 - 6 = 26 swim at least one stroke. Then 30 - 26 = 4 swim neither. The tempting trap is doing 32 - 30 = 2, which ignores the overlap of 6.

Question 2

Amira and Ben share $80 in the ratio 3:5. After Amira gives Ben $6, how much more does Ben have than Amira?

  1. $16
  2. $20
  3. $24
  4. $32 (correct answer)
Explanation: Split $80 into 8 parts, so each part is $10. Amira starts with 3 parts = $30 and Ben starts with 5 parts = $50. After Amira gives Ben $6, Amira has $24 and Ben has $56. Ben has $56 - $24 = $32 more. The tempting $20 is the original gap before the $6 transfer, which actually changes the difference by $12, not $0.

Question 3

The average of 6 numbers is 14. After removing one number, the average of the other 5 is 12. What number was removed?

  1. 12
  2. 16
  3. 24 (correct answer)
  4. 26
Explanation: The original 6 numbers total 6 times 14, or 84. The remaining 5 numbers total 5 times 12, or 60. Subtracting gives 84 - 60 = 24, so the removed number is 24. A common error is to subtract 14 - 12 = 2 and pick a small value, forgetting to multiply by the counts.

Question 4

Twice the smallest of three consecutive integers is 14 more than the largest. What is the middle integer?

  1. 16
  2. 17 (correct answer)
  3. 18
  4. 19
Explanation: Let the smallest be x, so the integers are x, x+1, x+2. Twice the smallest is 2x, and 14 more than the largest is x+16. Set 2x = x+16, so x = 16. The middle integer is x+1, which is 17. The trap is choosing 16, but that is the smallest, not the middle.

Question 5

Two identical shirts and a belt cost $90. The belt costs $15 less than one shirt. What is the price of one shirt?

  1. $25
  2. $30
  3. $35 (correct answer)
  4. $45
Explanation: Let one shirt be s. The belt is s - 15, so 2s + (s - 15) = 90. That means 3s - 15 = 90, so 3s = 105 and s = 35. A tempting wrong answer is $30, because that would make two shirts $60 and the belt $15, totaling only $75, not $90.

Question 6

A machine produces bolts at a rate that decreases by 10% each hour due to wear. If it produces 100 bolts in the first hour, how many bolts will it produce in the fourth hour?

  1. 72.9 bolts (correct answer)
  2. 70.0 bolts
  3. 65.6 bolts
  4. 59.0 bolts
Explanation: When you encounter a problem about rates that decrease by a fixed percentage each time period, you're dealing with exponential decay. The key insight is that each hour, the machine produces 90% of what it produced the previous hour (since it decreases by 10%). To find the production in the fourth hour, you need to track the hourly output. Starting with 100 bolts in hour 1:
  • Hour 2: 100×0.9=90100 \times 0.9 = 90 bolts
  • Hour 3: 90×0.9=8190 \times 0.9 = 81 bolts
  • Hour 4: 81×0.9=72.981 \times 0.9 = 72.9 bolts
Alternatively, you can use the formula: Hour 4=100×(0.9)3=100×0.729=72.9\text{Hour 4} = 100 \times (0.9)^3 = 100 \times 0.729 = 72.9 bolts. Choice A (72.9 bolts) is correct. Choice B (70.0 bolts) likely comes from incorrectly calculating 100 × 0.7, which would be a 30% decrease total rather than 10% each hour. Choice C (65.6 bolts) might result from miscalculating the exponential decay or confusing the number of reductions. Choice D (59.0 bolts) appears to come from applying too many reductions or using an incorrect percentage. Remember that in exponential decay problems, you multiply by the same factor repeatedly—here, 0.9 for each hour that passes. Don't confuse this with linear decrease, where you'd subtract the same amount each time. Always identify whether the percentage applies to each individual period or cumulatively.

Question 7

A rectangular garden is surrounded by a walking path of uniform width. The garden itself is 20 feet by 30 feet. If the total area including the path is 1,064 square feet, what is the width of the path?

  1. 2 feet
  2. 3 feet
  3. 4 feet (correct answer)
  4. 5 feet
Explanation: Let w be the width of the path. The path adds w to each side, so the outer rectangle is (20 + 2w) feet by (30 + 2w) feet. Set its area equal to the total: (20 + 2w)(30 + 2w) = 1,064. Expanding gives 600 + 100w + 4w² = 1,064, so 4w² + 100w − 464 = 0. Divide by 4: w² + 25w − 116 = 0. This factors as (w + 29)(w − 4) = 0, so w = 4 (a width cannot be negative). Check: 20 + 8 = 28 and 30 + 8 = 38, and 28 × 38 = 1,064 square feet. A common mistake is adding w only once to each dimension. Testing the other widths shows they do not fit: a 3-foot path gives 26 × 36 = 936, and a 5-foot path gives 30 × 40 = 1,200. The width of the path is 4 feet.

Question 8

In a chess tournament, each player plays every other player exactly once. If there are 28 total games played, and the tournament director wants to add the minimum number of players so that the total games played becomes a perfect square, how many additional players should be added?

  1. 1 player (correct answer)
  2. 2 players
  3. 3 players
  4. 4 players
Explanation: When you see a chess tournament problem, you're dealing with combinations - specifically, choosing 2 players from n total players to form each game. The formula for this is n(n−1)2\frac{n(n-1)}{2}, where n is the number of players. Since there are 28 games total, you can set up the equation: n(n−1)2=28\frac{n(n-1)}{2} = 28, which gives you n(n−1)=56n(n-1) = 56. Testing values, you'll find that when n = 8, you get 8×7=568 \times 7 = 56. So there are currently 8 players. Now you need to find the minimum number of additional players to make the total games a perfect square. The next perfect squares after 28 are 36, 49, 64, etc. For each perfect square, you need to check if it corresponds to a valid number of players. For 36 games: n(n−1)=72n(n-1) = 72, which gives approximately n = 8.97 (not a whole number) For 49 games: n(n−1)=98n(n-1) = 98, which gives approximately n = 10.4 (not a whole number)
For 36 games: Let's recalculate more carefully. We need n(n−1)2=36\frac{n(n-1)}{2} = 36, so n(n−1)=72n(n-1) = 72. This doesn't yield a whole number solution. Actually, for 36 games: n(n−1)=72n(n-1) = 72. Trying n = 9: 9×8=729 \times 8 = 72. Perfect! So 9 players would create 36 games. Going from 8 to 9 players means adding 1 player, making A correct. B, C, and D would result in 10, 11, or 12 players respectively, creating 45, 55, or 66 games - none of which are perfect squares. Remember: In combination problems, always check if your final answer yields a whole number of objects.

Question 9

A parking garage charges $3 for the first hour and $2 for each additional hour or fraction thereof. If the maximum daily charge is $15, and Elena parks for 8.5 hours, how much would she save by parking for exactly 8 hours instead?

  1. $0 (correct answer)
  2. $1
  3. $2
  4. $3
Explanation: When you encounter parking fee problems with maximum daily charges, you need to calculate the cost under normal rules first, then check if the maximum applies. Let's calculate Elena's cost for 8.5 hours. The garage charges $3 for the first hour plus $2 for each additional hour or fraction thereof. For 8.5 hours, she pays for the first hour plus 8 additional hours (since any fraction counts as a full hour). That's $3+(8×2)=3+16=193 + (8 \times 2) = 3 + 16 = 19 $ dollars. However, since the maximum daily charge is $15, Elena actually pays $15. For exactly 8 hours, she'd pay $3+(73 + (7 \times$ 2) = 3 + 14 = 17$$ dollars. Again, this exceeds the $15 maximum, so she'd pay $15. Since Elena pays $15 in both scenarios, her savings would be $$15 - 15 = 0$$ dollars. Choice A ($0) is correct because both parking durations result in the maximum charge being applied. Choice B (1)incorrectlyassumesthedifferencebetweenthecalculatedfeeswithoutconsideringthemaximum.ChoiceC(1) incorrectly assumes the difference between the calculated fees without considering the maximum. Choice C (2) represents the additional hourly charge but ignores that the maximum cap applies to both scenarios. Choice D ($3) might result from miscalculating the hourly structure or confusing the first-hour fee with the savings. Always check whether maximum fee limits apply in multi-step pricing problems. Calculate the "normal" cost first, then apply any caps or limits. The maximum often eliminates differences you might expect between similar scenarios.

Question 10

In a school election, candidate A received 40% of the votes, candidate B received 35%, and candidate C received the remaining votes. If candidate A won by 120 votes over candidate B, how many total votes were cast?

  1. 1,800 votes
  2. 2,000 votes
  3. 2,400 votes (correct answer)
  4. 2,800 votes
Explanation: When you encounter percentage problems with vote differences, you need to translate the percentage gap into actual votes to find the total. Let's set up the problem systematically. If the total votes cast is xx, then candidate A received 0.40x0.40x votes and candidate B received 0.35x0.35x votes. Since A won by 120 votes over B, you can write: 0.40x−0.35x=1200.40x - 0.35x = 120 Simplifying: 0.05x=1200.05x = 120 Solving for xx: x=1200.05=2400x = \frac{120}{0.05} = 2400 Let's verify: With 2,400 total votes, A received 0.40×2400=9600.40 \times 2400 = 960 votes and B received 0.35×2400=8400.35 \times 2400 = 840 votes. The difference is indeed 960−840=120960 - 840 = 120 votes. Now for the wrong answers: Choice A (1,800) would give A only 720 votes and B 630 votes, creating a 90-vote difference—too small. Choice B (2,000) would result in A getting 800 votes and B getting 700 votes, producing only a 100-vote difference. Choice D (2,800) would give A 1,120 votes and B 980 votes, creating a 140-vote difference—too large. Strategy tip: In percentage difference problems, always convert the percentage gap to an equation using the total as your variable. The key insight is that a 5% difference (40% - 35%) equals 120 actual votes, which allows you to solve for the total. Double-check by calculating the actual vote counts to ensure they match the given conditions.

Question 11

A delivery truck travels at 50 mph on highways and 25 mph in city traffic. On a 200-mile route, the truck spends twice as much time in city traffic as on highways. What is the total travel time for this route?

  1. 5 hours
  2. 6 hours (correct answer)
  3. 7 hours
  4. 8 hours
Explanation: When you encounter word problems involving distance, speed, and time with multiple conditions, set up equations using the fundamental relationship: distance = speed × time, or rearranged as time = distance ÷ speed. Let's define variables: let hh = time spent on highways and cc = time in city traffic. You're told that c=2hc = 2h (twice as much time in city traffic). For distance calculations: Highway distance = 50h50h miles, and city distance = 25c=25(2h)=50h25c = 25(2h) = 50h miles. Since the total route is 200 miles: 50h+50h=20050h + 50h = 200, which gives us 100h=200100h = 200, so h=2h = 2 hours. Therefore: c=2h=4c = 2h = 4 hours, and total time = h+c=2+4=6h + c = 2 + 4 = 6 hours. Choice A (5 hours) likely results from incorrectly assuming equal time splits or miscalculating the distance relationship. Choice C (7 hours) might come from setting up the time relationship backwards or adding an extra hour due to computational error. Choice D (8 hours) could result from incorrectly assuming the truck spends twice as much distance (rather than time) in city traffic, or from misapplying the speed-time relationships. The correct answer is B (6 hours). Strategy tip: In multi-step motion problems, always clearly define your variables first, then translate each condition into an equation. Double-check by verifying that your distances add up to the total given distance—this catches most algebraic errors.

Question 12

A bakery makes three types of cookies: chocolate chip, oatmeal, and sugar. The profit margins are $0.50, $0.40, and $0.30 per cookie respectively. If they sell 200 cookies daily with the ratio of chocolate chip to oatmeal to sugar being 3:2:5, what is their daily profit from cookie sales?

  1. $73
  2. $76 (correct answer)
  3. $79
  4. $82
Explanation: When you encounter ratio problems with profit calculations, break them down into two steps: first determine the actual quantities from the ratio, then apply the profit margins to find total earnings. Given the 3:2:5 ratio for chocolate chip to oatmeal to sugar cookies, you need to find how many parts the ratio represents: 3+2+5=103 + 2 + 5 = 10 total parts. With 200 cookies sold daily, each part equals 200÷10=20200 ÷ 10 = 20 cookies. This means they sell:
  • Chocolate chip: 3×20=603 × 20 = 60 cookies at $0.50 profit each
  • Oatmeal: $2×20=402 × 20 = 40 $ cookies at $0.40 profit each
  • Sugar: $$5 × 20 = 100$$ cookies at $0.30 profit each
Calculate the profit for each type:
  • Chocolate chip: $$60 × 0.50 = 30$$
  • Oatmeal: 40×0.40=1640 × 0.40 = 16
  • Sugar: 100×0.30=30100 × 0.30 = 30
Total daily profit: 30+16+30=7630 + 16 + 30 = 76 Choice A (73)likelyresultsfrommiscalculatingtheratioportionsormakingarithmeticerrorsinthemultiplication.ChoiceC(73) likely results from miscalculating the ratio portions or making arithmetic errors in the multiplication. Choice C (79) might come from switching profit margins between cookie types or adding incorrectly. Choice D ($82) could result from using the wrong total number of cookies or misapplying the ratios entirely. For ratio problems on the HSPT, always verify that your individual quantities add up to the given total before proceeding with calculations. This catches errors early and ensures your profit calculations are based on correct amounts.

Question 13

Two trains leave stations 300 miles apart at the same time, traveling toward each other. Train A travels at 45 mph and Train B at 55 mph. If Train A makes a 30-minute stop after traveling for 2 hours, how long after their departure will they meet?

  1. 2 hours 45 minutes
  2. 3 hours 13.5 minutes (correct answer)
  3. 3 hours 30 minutes
  4. 3 hours 45 minutes
Explanation: When two trains move toward each other, their speeds add, so the gap closes at 45+55=10045 + 55 = 100 mph while both are moving. In the first 2 hours the trains cover 100×2=200100 \times 2 = 200 miles, leaving 300−200=100300 - 200 = 100 miles between them. During Train A's 30-minute stop, only Train B moves, covering 55×0.5=27.555 \times 0.5 = 27.5 miles. The gap is now 100−27.5=72.5100 - 27.5 = 72.5 miles. Both trains then close the gap at 100100 mph, which takes 72.5÷100=0.72572.5 \div 100 = 0.725 hours, or 43.543.5 minutes. The total is 2 hours + 30 minutes + 43.5 minutes = 3 hours 13.5 minutes. An answer of 3 hours 30 minutes adds the full stop to the 3-hour no-stop time, forgetting that Train B kept closing the gap during the stop. An answer of 3 hours 45 minutes is later still. An answer of 2 hours 45 minutes is too early: at that point the trains are still more than 70 miles apart.

Question 14

A water tank is being filled by three pipes. Pipe A fills 16\frac{1}{6} of the tank per hour, Pipe B fills 18\frac{1}{8} of the tank per hour, and Pipe C drains 112\frac{1}{12} of the tank per hour. If all three pipes operate simultaneously starting with an empty tank, how long will it take to fill 34\frac{3}{4} of the tank?

  1. 4.5 hours exactly
  2. 3.6 hours exactly (correct answer)
  3. 6.0 hours exactly
  4. 2.4 hours exactly
Explanation: When you encounter work rate problems involving multiple pipes or workers, you need to combine their individual rates to find the net rate of work being done. First, find the combined rate. Pipe A fills 16\frac{1}{6} of the tank per hour, Pipe B fills 18\frac{1}{8} per hour, and Pipe C drains 112\frac{1}{12} per hour. Since Pipe C drains water, you subtract its rate: 16+18−112\frac{1}{6} + \frac{1}{8} - \frac{1}{12}. To add these fractions, find a common denominator of 24: 424+324−224=524\frac{4}{24} + \frac{3}{24} - \frac{2}{24} = \frac{5}{24} of the tank per hour. Now use the formula: Time = Work ÷ Rate. To fill 34\frac{3}{4} of the tank at a rate of 524\frac{5}{24} per hour: 34÷524=34×245=7220=3.6\frac{3}{4} ÷ \frac{5}{24} = \frac{3}{4} × \frac{24}{5} = \frac{72}{20} = 3.6 hours. Answer B (3.6 hours) is correct. Answer A (4.5 hours) likely results from calculation errors with the fractions. Answer C (6.0 hours) might come from using only Pipe A's rate (34÷16=4.5\frac{3}{4} ÷ \frac{1}{6} = 4.5, but this still doesn't equal 6). Answer D (2.4 hours) could result from adding Pipe C's rate instead of subtracting it, giving 724\frac{7}{24} per hour. Remember: when pipes drain or workers slow down the process, subtract their rates from the positive rates. Always double-check your fraction arithmetic in work rate problems.

Question 15

Two workers can complete a job together in 12 hours. Working alone, one worker takes 10 hours longer than the other to complete the same job. How long would the faster worker take to complete the job alone?

  1. 18 hours working alone
  2. 20 hours working alone (correct answer)
  3. 24 hours working alone
  4. 16 hours working alone
Explanation: In work problems, add the rates: each worker's rate is the fraction of the job done per hour. Let the faster worker take xx hours, so the slower one takes x+10x + 10 hours. Together they finish in 12 hours: 1x+1x+10=112\frac{1}{x} + \frac{1}{x + 10} = \frac{1}{12} Test x=20x = 20: 120+130=360+260=560=112\frac{1}{20} + \frac{1}{30} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}. It works, so the faster worker takes 20 hours and the slower worker takes 30 hours. An answer of 24 hours is what each worker would take if they worked at the same speed, which ignores the 10-hour difference. With 18 hours, the pair would take 118+128=23252\frac{1}{18} + \frac{1}{28} = \frac{23}{252} of the job per hour, or about 11 hours, which is too fast. With 16 hours, they would take under 10 hours. The faster worker takes 20 hours.

Question 16

A water tank can be filled by three pipes. Pipe A alone can fill the tank in 12 hours, Pipe B alone can fill it in 15 hours, and Pipe C alone can fill it in 20 hours. If all three pipes work together for 3 hours, then Pipe A is shut off and only Pipes B and C continue working, how many additional hours will it take to completely fill the tank, rounded to the nearest tenth of an hour?

  1. It will take an additional 2.4 hours to fill the tank completely
  2. It will take an additional 3.4 hours to fill the tank completely (correct answer)
  3. It will take an additional 4.2 hours to fill the tank completely
  4. It will take an additional 5.1 hours to fill the tank completely
Explanation: Change each pipe's time into a rate. Pipe A fills 112\frac{1}{12} of the tank per hour, Pipe B 115\frac{1}{15}, and Pipe C 120\frac{1}{20}. Together: 560+460+360=1260=15\frac{5}{60} + \frac{4}{60} + \frac{3}{60} = \frac{12}{60} = \frac{1}{5} per hour. In 3 hours the three pipes fill 3×15=353 \times \frac{1}{5} = \frac{3}{5} of the tank, leaving 25\frac{2}{5}. Pipes B and C together fill 460+360=760\frac{4}{60} + \frac{3}{60} = \frac{7}{60} per hour. The time for the rest is 25÷760=25×607=247≈3.43\frac{2}{5} \div \frac{7}{60} = \frac{2}{5} \times \frac{60}{7} = \frac{24}{7} \approx 3.43 hours, which rounds to 3.4 hours. If you mix up the filled part and the empty part and divide 35\frac{3}{5} by 760\frac{7}{60}, you get about 5.1 hours. Rounding 3.43 up to 3.6 is a rounding slip. It will take an additional 3.4 hours.

Question 17

A machine produces widgets at a constant rate. In the first 4 hours, it produces 320 widgets. Due to a technical adjustment, its production rate increases by 25% for the next 6 hours. After that, a minor malfunction reduces its rate to 80% of the original rate for the final 2 hours of operation. What is the total number of widgets produced during the entire 12-hour period?

  1. The machine produced a total of 1,048 widgets during the 12-hour period (correct answer)
  2. The machine produced a total of 1,152 widgets during the 12-hour period
  3. The machine produced a total of 1,248 widgets during the 12-hour period
  4. The machine produced a total of 1,344 widgets during the 12-hour period
Explanation: Find the original rate first: 320 widgets ÷ 4 hours = 80 widgets per hour. Next 6 hours: the rate rises 25%, so it is 80 × 1.25 = 100 widgets per hour, and the machine makes 100 × 6 = 600 widgets. Final 2 hours: the rate is 80% of the original rate, so 80 × 0.80 = 64 widgets per hour, and it makes 64 × 2 = 128 widgets. Total: 320 + 600 + 128 = 1,048 widgets. A quick check rules out the larger totals. The fastest the machine ever runs is 100 per hour, so 12 hours can give at most 1,200 widgets. A total of 1,344 would need 112 per hour for all 12 hours, and 1,248 would need 104 per hour, so both are impossible. A total of 1,152 would need an average of 96 per hour, but the machine runs at 100 per hour for only half the time. The machine produced a total of 1,048 widgets.

Question 18

A recipe calls for ingredients in the ratio 4:3:2 for flour, sugar, and butter respectively. If a baker wants to make a batch that uses exactly 2.5 cups of butter, and flour costs $0.80 per cup while sugar costs $1.20 per cup, what will be the combined cost of the flour and sugar needed?

  1. The combined cost of flour and sugar will be $8.50 (correct answer)
  2. The combined cost of flour and sugar will be $9.00
  3. The combined cost of flour and sugar will be $9.50
  4. The combined cost of flour and sugar will be $10.00
Explanation: When you encounter ratio problems, think about proportional relationships - ratios tell you how quantities relate to each other, not their absolute values. Here you need to scale the entire recipe based on one known ingredient. The ratio 4:3:2 means for every 4 cups of flour, you need 3 cups of sugar and 2 cups of butter. Since you're using 2.5 cups of butter instead of the base amount of 2 cups, you need to find the scaling factor: 2.5÷2=1.252.5 ÷ 2 = 1.25 This means you're making 1.25 times the original recipe. Scale up the other ingredients accordingly:
  • Flour needed: 4×1.25=54 × 1.25 = 5 cups
  • Sugar needed: 3×1.25=3.753 × 1.25 = 3.75 cups
Now calculate the costs:
  • Flour cost: 5×$0.80=$4.005 × \$0.80 = \$4.00
  • Sugar cost: 3.75×$1.20=$4.503.75 × \$1.20 = \$4.50
  • Combined cost: $4.00+$4.50=$8.50\$4.00 + \$4.50 = \$8.50
Answer A (8.50)iscorrect.AnswerB(8.50) is correct. Answer B (9.00) likely comes from miscalculating the sugar amount as 4 cups instead of 3.75. Answer C (9.50)mightresultfromusingincorrectingredientratiosorwrongscalingfactors.AnswerD(9.50) might result from using incorrect ingredient ratios or wrong scaling factors. Answer D (10.00) could come from multiple calculation errors, such as using the wrong ratio or incorrectly applying the scaling factor. Remember: in ratio problems, always identify your scaling factor first by comparing the given quantity to its ratio value, then apply that same factor to all other components before doing any cost calculations.

Question 19

A rectangular swimming pool is being filled with water. The pool is 25 feet long, 15 feet wide, and 6 feet deep. Water flows in at a rate of 150 cubic feet per hour, but due to evaporation and small leaks, water is lost at a rate of 18 cubic feet per hour. If the pool starts empty, how many hours will it take to fill the pool to 80% of its capacity?

  1. It will take approximately 13.6 hours to reach 80% capacity (correct answer)
  2. It will take approximately 16.4 hours to reach 80% capacity
  3. It will take approximately 19.1 hours to reach 80% capacity
  4. It will take approximately 21.8 hours to reach 80% capacity
Explanation: When you encounter word problems involving rates and capacity, you need to identify the net rate of change and the target volume. This problem combines geometry (finding volume) with rate calculations. First, calculate the pool's total volume: 25×15×6=2,25025 \times 15 \times 6 = 2,250 cubic feet. Since you need 80% capacity, your target is 2,250×0.8=1,8002,250 \times 0.8 = 1,800 cubic feet. Next, determine the net rate of water accumulation. Water flows in at 150 cubic feet per hour but is lost at 18 cubic feet per hour, giving you a net rate of 150−18=132150 - 18 = 132 cubic feet per hour. Finally, divide the target volume by the net rate: 1,800132=13.636...\frac{1,800}{132} = 13.636... hours, which rounds to approximately 13.6 hours. This confirms answer A is correct. Answer B (16.4 hours) likely results from forgetting to subtract the water loss rate and using only 110 cubic feet per hour as the filling rate. Answer C (19.1 hours) might come from incorrectly calculating the pool volume or using the wrong capacity percentage. Answer D (21.8 hours) could result from multiple errors, such as miscalculating both the volume and failing to account for the net rate properly. Strategy tip: In rate problems with gains and losses, always calculate the net rate first. Don't forget that "filling" problems often involve both inflow and outflow rates that must be combined algebraically.

Question 20

A store is having a clearance sale. All items are first marked down by 30%, then an additional 20% is taken off the already reduced price. If a jacket originally costs $150, and there is also a 6.5% sales tax applied to the final discounted price, what is the total amount a customer will pay for the jacket?

  1. The customer will pay a total of $89.04 for the jacket
  2. The customer will pay a total of $89.46 for the jacket (correct answer)
  3. The customer will pay a total of $89.88 for the jacket
  4. The customer will pay a total of $90.30 for the jacket
Explanation: When you encounter multi-step discount problems, work through each percentage change sequentially—never add the percentages together, as they compound. Start with the original price of $150. The first markdown is 30%, so the jacket is reduced by $150 \times 0.30 = \45 , making the new price 150 - 45 = $105 . Next, an additional 20% comes off this already-reduced price of $105. The second discount is $105 \times 0.20 = \21,bringingthepricedownto, bringing the price down to 105 - 21 = $84$$. Finally, apply the 6.5% sales tax to this final discounted price: 84×0.065=$5.4684 \times 0.065 = \$5.46. The total amount paid is 84+5.46=$89.4684 + 5.46 = \$89.46. Answer B (89.46)iscorrect.AnswerA(89.46) is correct. Answer A (89.04) likely results from calculation errors in the discount steps. Answer C (89.88)mightcomefromapplyingthetaxincorrectlyormakingroundingerrors.AnswerD(89.88) might come from applying the tax incorrectly or making rounding errors. Answer D (90.30) could result from adding the discount percentages (50% total) instead of applying them sequentially, or from other computational mistakes. The key insight is that sequential discounts don't simply add up—a 30% discount followed by a 20% discount is not the same as a 50% discount. Each percentage applies to the current price at that step. Always calculate step-by-step and remember that sales tax applies to the final discounted price, not the original price.