Practice Test 6 - 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 $7, 14, 28, 56, 112, ...$ continues with the same rule. What is the 8th term?
2. Compare the quantities: (a) $\frac{5}{6} \div \frac{5}{12}$ and (b) $2$
3. Compare the quantities: (a) $5^2 - 4^2$ and (b) $3^2$
4. In the sequence $5, 15, 45, 135, 405, ...$ each term follows the same rule. What is the 7th term?
5. Compare the quantities: (a) $4! - 3!$ and (b) $3^3 - 2^3$
6. A construction crew is building a circular patio with a radius of 8 feet. They plan to install a decorative border around the entire circumference that costs $15 per foot. Additionally, they will cover the patio surface with special tiles that cost $8 per square foot. Using π ≈ 3.14, what is the total cost for both the border and the tiles?
7. At a book fair, fiction books cost $8 each and non-fiction books cost $12 each. Sarah bought some books and spent exactly $96. If she bought at least one book of each type, and the number of fiction books she bought was a multiple of 3, how many different combinations of books could she have purchased?
8. Compare the quantities: (a) $3^4 - 2^5$ and (b) $4^3 - 5^2$
9. 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?
10. Compare the quantities: (a) $(-3)^2 + (-2)^3$ and (b) $(-1)^4 + (-5)^2$
11. Compare the quantities: (a) $\frac{3}{4} \times \frac{8}{9}$ and (b) $\frac{2}{3}$
12. The average of 6 numbers is 14. After removing one number, the average of the other 5 is 12. What number was removed?
13. Circle (a) has radius 3, circle (b) has diameter 8, and circle (c) has circumference $12\pi$. Which statement about their areas is correct?
14. The sequence $1, 3, 7, 15, 31, 63, ...$ continues with the same pattern. What is the next term?
15. A basketball player's free throw percentage follows this pattern: in practice, she makes 85% of her shots, but during games, her percentage drops by 15 percentage points due to pressure. In a recent game, she attempted 20 free throws. Based on her expected game performance, approximately how many free throws would she be expected to miss?
16. Two identical shirts and a belt cost $90. The belt costs $15 less than one shirt. What is the price of one shirt?
17. Compare the values: (A) $1.8 \times 2.5$ and (B) $\frac{9}{2} \times \frac{4}{5}$
18. In the sequence $2, 9, 23, 44, 72, 107, ...$ what pattern governs the terms, and what is the next value?
19. In the sequence $3, 7, 15, 31, 63, ...$ each term after the first is formed by a specific rule. What is the next term?
20. Compare (a) $6^3 \cdot 6^2$ with (b) $(6^2)^3$.

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