SHSAT Math Quiz: Multi Step Problem Solving
10 questions · exam conditions
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Multi Step Problem SolvingQuestion 1 of 10

A movie theater has 240 seats arranged in rows with an equal number of seats per row. If there are 8 more rows than there are seats per row, how many seats are in each row?

20 seats
16 seats
10 seats
12 seats
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SHSAT Math Quiz

SHSAT Math Quiz: Multi Step Problem Solving

Practice Multi Step Problem Solving 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 Multi Step Problem Solving, 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 movie theater has 240 seats arranged in rows with an equal number of seats per row. If there are 8 more rows than there are seats per row, how many seats are in each row?

  1. 20 seats
  2. 16 seats
  3. 10 seats
  4. 12 seats (correct answer)
Explanation: This is a classic "system of equations" word problem where you need to translate the given information into mathematical relationships. When you see problems involving arrangements with constraints between dimensions, set up variables for the unknowns and use the given relationships. Let's call the number of seats per row ss and the number of rows rr. The total seats gives us: s×r=240s \times r = 240. The constraint "8 more rows than seats per row" means: r=s+8r = s + 8. Substituting the second equation into the first: s(s+8)=240s(s + 8) = 240. Expanding: s2+8s=240s^2 + 8s = 240, or s2+8s−240=0s^2 + 8s - 240 = 0. Using the quadratic formula or factoring: (s+20)(s−12)=0(s + 20)(s - 12) = 0. This gives s=12s = 12 or s=−20s = -20. Since seats can't be negative, s=12s = 12. Let's verify: 12 seats per row, so r=12+8=20r = 12 + 8 = 20 rows. Total: 12×20=24012 \times 20 = 240 seats ✓ Choice A (20 seats) would give 28 rows and 20×28=56020 \times 28 = 560 total seats—too many. Choice B (16 seats) would give 24 rows and 16×24=38416 \times 24 = 384 seats—also too many. Choice C (10 seats) would give 18 rows and 10×18=18010 \times 18 = 180 seats—too few. Strategy tip: In constraint problems like this, always check your answer by substituting back into all original conditions. Many students solve correctly but pick the wrong variable or forget to verify their solution matches the problem's requirements.

Question 2

Olivia is filling gift bags with the same assortment of candies. She has 240 chocolate pieces, 180 caramels, and 60 mints. If she wants to use all of the candy and each bag must contain the same number of each type, what is the greatest number of gift bags Olivia can make?

  1. 60 (correct answer)
  2. 40
  3. 30
  4. 20
Explanation: When you see a problem about distributing items equally into groups while using everything, you're looking for the Greatest Common Factor (GCF). This tells you the largest number of identical groups you can make. To find the GCF of 240, 180, and 60, start by finding the prime factorization of each number:
  • 240 = 2⁴ × 3 × 5
  • 180 = 2² × 3² × 5
  • 60 = 2² × 3 × 5
The GCF uses the lowest power of each common prime factor: 2² × 3 × 5 = 4 × 3 × 5 = 60. This means Olivia can make 60 gift bags, with each bag containing 4 chocolate pieces (240 ÷ 60), 3 caramels (180 ÷ 60), and 1 mint (60 ÷ 60). Looking at the wrong answers: Choice B (40) seems reasonable but doesn't divide evenly into 180 - you'd get 4.5 caramels per bag, which is impossible. Choice C (30) would require 8 chocolates, 6 caramels, and 2 mints per bag, but 180 ÷ 30 = 6, not the needed 6 caramels. Choice D (20) would need 12 chocolates, 9 caramels, and 3 mints per bag, but again the division doesn't work cleanly for all three candy types. Strategy tip: On GCF problems involving distribution, always verify your answer by dividing each original quantity by your proposed number of groups. If any division results in a fraction or doesn't match the required distribution, you haven't found the correct GCF.

Question 3

A passenger train leaves City A traveling toward City B at 60 miles per hour. Two hours later, a freight train leaves City A on the same track traveling 80 miles per hour. How far from City A will the passenger train be when the freight train catches up to it?

  1. 480 miles (correct answer)
  2. 440 miles
  3. 360 miles
  4. 300 miles
Explanation: When you see two objects starting from the same point at different times and speeds, you're dealing with a "catch-up" problem. The key insight is that both trains will have traveled the same distance when the freight train catches up. Let's set up the problem systematically. Let tt = the time (in hours) the passenger train travels before being caught. Since the freight train starts 2 hours later, it travels for (t−2)(t-2) hours. Using the formula Distance = Speed × Time:
  • Passenger train distance: 60t60t
  • Freight train distance: 80(t−2)80(t-2)
At the catch-up point, these distances are equal: 60t=80(t−2)60t = 80(t-2) 60t=80t−16060t = 80t - 160 −20t=−160-20t = -160 t=8t = 8 The passenger train travels for 8 hours, covering 60×8=48060 \times 8 = 480 miles. Looking at the wrong answers: Choice B (440 miles) might result from calculation errors in the algebra. Choice C (360 miles) could come from incorrectly using 6 hours instead of 8, perhaps from solving 60t=80t60t = 80t without accounting for the 2-hour head start. Choice D (300 miles) might result from using just the freight train's travel time (80×3.75=30080 \times 3.75 = 300) without proper setup. The correct answer is A) 480 miles. Strategy tip: In catch-up problems, always define your variable as the total time for the object that started first, then subtract the head start time for the second object. Setting distances equal is your key equation.

Question 4

Maria saves money for a laptop by depositing $45 each week into her account. After 8 weeks, she realizes she needs to save an additional $180 to afford the laptop she wants. If she increases her weekly deposits to $60, how many more weeks will it take her to save the additional amount needed?

  1. 2 weeks
  2. 3 weeks (correct answer)
  3. 4 weeks
  4. 5 weeks
Explanation: Maria has already saved $45 × 8 = $360. She needs an additional $180. At her new rate of $60 per week, she needs $180 ÷ $60 = 3 weeks. Choice A assumes she continues at the old rate for 2 weeks. Choice C incorrectly calculates using the original deposit amount. Choice D adds the original 8 weeks incorrectly to the calculation.

Question 5

A store offers a 25% discount on all items, then applies an additional 8% sales tax to the discounted price. If Marcus buys a jacket originally priced at $120 and pays with a $100 bill, how much change should he receive?

  1. $2.80 (correct answer)
  2. $97.20
  3. $3.20
  4. $2.20
Explanation: Original price: $120. After 25% discount: $120 × 0.75 = $90. After 8% tax on discounted price: $90 × 1.08 = $97.20. Change from $100: $100 - $97.20 = $2.80. Choice B gives the final price, not change. Choice C applies tax before discount. Choice D calculates tax on original price then applies discount.

Question 6

A recipe for trail mix calls for nuts, dried fruit, and chocolate chips in the ratio 5:3:2. If Sarah wants to make 4 pounds of trail mix but only has 12 ounces of chocolate chips available, how many ounces of nuts will she need to use all her chocolate chips?

  1. 30 ounces (correct answer)
  2. 20 ounces
  3. 18 ounces
  4. 24 ounces
Explanation: Ratio is nuts:fruit:chips = 5:3:2. If chocolate chips = 12 ounces represents 2 parts, then 1 part = 6 ounces. Therefore nuts = 5 parts = 5 × 6 = 30 ounces. Choice B assumes 1 part = 4 ounces. Choice C confuses the ratio positions. Choice D uses incorrect proportional reasoning.

Question 7

A printer can produce 45 pages in 3 minutes when set to draft mode. At that rate, how many pages can it print in 25 minutes?

  1. 325
  2. 355
  3. 375 (correct answer)
  4. 405
Explanation: This is a unit rate problem where you need to find how much work gets done per unit of time, then scale it up. When you see questions asking "at that rate" or "at this speed," you're dealing with proportional relationships. First, find the printer's rate per minute. If it prints 45 pages in 3 minutes, divide to get the unit rate: 45 pages3 minutes=15 pages per minute\frac{45 \text{ pages}}{3 \text{ minutes}} = 15 \text{ pages per minute} Now multiply this rate by 25 minutes: 15×25=375 pages15 \times 25 = 375 \text{ pages} Looking at the wrong answers reveals common calculation errors. Choice A (325) likely comes from incorrectly calculating the rate as 13 pages per minute instead of 15, then multiplying by 25. Choice B (355) might result from arithmetic mistakes in the multiplication step. Choice D (405) could come from miscalculating the initial rate as 16 pages per minute or making errors in the final multiplication. The correct answer is C (375 pages). Strategy tip: For rate problems on the SHSAT, always establish your unit rate first (amount per single unit of time), then multiply by the target time. Write out your rate calculation clearly - most errors happen when students try to set up complex proportions instead of finding the simple per-minute or per-hour rate. Double-check your division and multiplication, as these problems often include answer choices that result from common arithmetic mistakes.

Question 8

A rectangular garden has a length that is 8 feet more than twice its width. If the perimeter of the garden is 64 feet and fencing costs $12 per foot, what is the total cost to fence the entire garden?

  1. $384
  2. $768 (correct answer)
  3. $432
  4. $576
Explanation: Let w = width. Then length = 2w + 8. Perimeter = 2(length + width) = 2(2w + 8 + w) = 2(3w + 8) = 6w + 16 = 64. Solving: 6w = 48, so w = 8 feet. Length = 2(8) + 8 = 24 feet. Perimeter = 64 feet. Total cost = 64 × $12 = $768. Choice A uses incorrect width calculation. Choice C miscalculates the length formula. Choice D uses wrong perimeter value.

Question 9

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 18 mph while Cyclist B travels at 22 mph. After how many hours will they be exactly 200 miles apart?

  1. 4 hours
  2. 8 hours
  3. 6 hours
  4. 5 hours (correct answer)
Explanation: When two objects move in opposite directions from the same starting point, you're dealing with a relative motion problem where their speeds add together to determine how quickly the distance between them grows. Since Cyclist A travels at 18 mph and Cyclist B travels at 22 mph in opposite directions, they're separating at a combined rate of 18+22=4018 + 22 = 40 mph. Think of it this way: from Cyclist A's perspective, Cyclist B is moving away at 40 mph, and vice versa. To find when they'll be 200 miles apart, use the distance formula: Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}. Rearranging: Time=DistanceRate=200 miles40 mph=5 hours\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{200 \text{ miles}}{40 \text{ mph}} = 5 \text{ hours} Let's examine why the other answers are incorrect: A) 4 hours would only create a separation of 40×4=16040 \times 4 = 160 miles, falling short of the target. B) 8 hours would result in 40×8=32040 \times 8 = 320 miles of separation, which overshoots significantly. C) 6 hours would create 40×6=24040 \times 6 = 240 miles of separation, also too much. Only D) 5 hours gives exactly 40×5=20040 \times 5 = 200 miles. For relative motion problems on the SHSAT, remember this key principle: when objects move in opposite directions, add their speeds; when they move in the same direction, subtract the slower speed from the faster one. This combined rate is what determines how quickly the distance between them changes.

Question 10

A parking meter charges $1.50 for the first hour and $0.75 for each additional 30-minute period. If Jennifer parks for 3 hours and 45 minutes, what is the total parking fee?

  1. $5.25
  2. $4.50
  3. $6.00 (correct answer)
  4. $5.75
Explanation: First hour costs $1.50. Remaining time: 3h 45min - 1h = 2h 45min = 5.5 additional 30-minute periods. Since partial periods count as full periods, she pays for 6 additional 30-minute periods. Additional cost: 6 × $0.75 = $4.50. Total: $1.50 + $4.50 = $6.00. Choice A doesn't round up partial periods. Choice B miscalculates additional periods. Choice D uses wrong base rate calculation.