Practice Test 4 - HSPT Quantitative

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. The sequence $2, 6, 12, 20, 30, 42, ...$ follows a specific pattern. What is the 8th term?
2. In the sequence $2, 3, 5, 9, 17, 33, \ldots$, what pattern rule generates the next term?
3. Regular hexagon (a) has side length 2, equilateral triangle (b) has side length 6, and regular pentagon (c) has side length 3. Which has the greatest perimeter?
4. Compare the values: (A) $\frac{5}{8} + \frac{1}{4} - \frac{1}{8}$ and (B) $\frac{7}{12} + \frac{1}{6} - \frac{1}{12}$
5. A subscription service offers three plans: Plan A costs $8 per month with no per-use fees. Plan B costs $5 per month plus $0.50 per use. Plan C costs $2 per month plus $1.20 per use. For exactly how many uses per month are Plans A and B equally expensive?
6. 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?
7. Compare the quantities: (a) $2^3 + 3^2$ and (b) $5^2 - 2^2$
8. Compare the values: (A) $\sqrt{64} + \sqrt{36} - \sqrt{25}$ and (B) $\sqrt{100} - \sqrt{9} + \sqrt{4}$
9. A water tank is being filled by three pipes. Pipe A fills $\frac{1}{6}$ of the tank per hour, Pipe B fills $\frac{1}{8}$ of the tank per hour, and Pipe C drains $\frac{1}{12}$ of the tank per hour. If all three pipes operate simultaneously starting with an empty tank, how long will it take to fill $\frac{3}{4}$ of the tank?
10. 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?
11. Compare the values: (A) $0.45 + \frac{7}{12}$ and (B) $\frac{5}{6} + 0.28$
12. Of 30 swimmers, 18 swim freestyle, 14 swim backstroke, and 6 swim both. How many swim neither?
13. 64, 32, 36, 18, 22, ?
14. A factory has two assembly lines. Line A produces 40 units per hour but has a 5% defect rate. Line B produces 35 units per hour but has a 2% defect rate. If both lines run for 8 hours, what is the total number of non-defective units produced?
15. Compare the values: (A) $4.2 \div 0.6$ and (B) $3.5 \div 0.5$
16. The sequence $1, 8, 27, 64, 125, ...$ follows a clear pattern. What is the next term?
17. In the sequence $3, 9, 21, 45, 93, ...$ what rule generates each term, and what comes next?
18. In the sequence $0, 1, 5, 14, 30, 55, ...$ what is the underlying pattern, and what comes next?
19. A parking garage charges $3 for the first hour, $2 for each additional hour up to 8 hours total, and $1 for each hour beyond 8 hours. If someone parks for exactly 11.5 hours, what is their total parking cost?
20. A store offers a bulk discount: buy 10-19 items and get 10% off, buy 20-29 items and get 15% off, buy 30+ items and get 20% off. Each item normally costs $4.50. What is the cost per item when buying exactly 25 items?

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