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Practice Test 5 - HSPT Quantitative

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

  1. Compare the values: (A) 144−81\sqrt{144} - \sqrt{81} and (B) 49+16\sqrt{49} + \sqrt{16}
  2. 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?
  3. In the sequence 1,4,10,20,35,56,...1, 4, 10, 20, 35, 56, ... each term has a specific relationship. What is the 7th term?
  4. 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?
  5. Compare the quantities: (a) 0.4×0.750.4 \times 0.75 and (b) 310\frac{3}{10}
  6. Rectangular prism (a) has dimensions 2×3×6, rectangular prism (b) has dimensions 1×4×9, and cube (c) has side length 3. Which comparison of surface areas is correct?
  7. Compare the values: (a)(a) 34⋅5223⋅32\frac{3^4 \cdot 5^2}{2^3 \cdot 3^2} and (b)(b) 72⋅1122⋅7\frac{7^2 \cdot 11}{2^2 \cdot 7}
  8. A library charges late fees as follows: $0.25 per day for the first 5 days, $0.50 per day for days 6-10, and $1.00 per day thereafter. If someone returns a book 18 days late, what is their total late fee?
  9. Consider the sequence: 12,23,34,45,…\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots. What is the sum of the 88th and 99th terms?
  10. Compare the values: (A) 23+322^3 + 3^2 and (B) 52−225^2 - 2^2
  11. Compare the expressions: (a)(a) 0.125×640.25×16\frac{0.125 \times 64}{0.25 \times 16} and (b)(b) 18×3214×8\frac{\frac{1}{8} \times 32}{\frac{1}{4} \times 8}
  12. Compare the values: (A) 79×1814\frac{7}{9} \times \frac{18}{14} and (B) 45×1512\frac{4}{5} \times \frac{15}{12}
  13. A sequence has the property that the sum of any three consecutive terms is always 3030. If the first term is 77 and the second term is 1111, what is the 88th term?
  14. In the sequence 5,8,14,26,50,...5, 8, 14, 26, 50, ... each term follows a specific pattern. What is the next term?
  15. Compare the quantities: (a) 37+47\frac{3}{7} + \frac{4}{7} and (b) 11
  16. Compare the values: (a)(a) 53−3352+5⋅3+32\frac{5^3 - 3^3}{5^2 + 5 \cdot 3 + 3^2} and (b)(b) 72−427+4\frac{7^2 - 4^2}{7 + 4}
  17. Consider the sequence 10,13,19,28,40,55,...10, 13, 19, 28, 40, 55, ... What is the next term?
  18. Amira and Ben share $80 in the ratio 3:5. After Amira gives Ben $6, how much more does Ben have than Amira?
  19. 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?
  20. 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?

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