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Practice Test 1 - HSPT Quantitative

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

  1. Compare the quantities: (a) 712×89\frac{7}{12} \times \frac{8}{9} and (b) 56×34\frac{5}{6} \times \frac{3}{4}
  2. Compare the values: (A) 25% of 8425\% \text{ of } 84 and (B) 30% of 7030\% \text{ of } 70
  3. The sequence 2,6,18,54,162,...2, 6, 18, 54, 162, ... follows a pattern. If this pattern continues, what is the 8th term?
  4. Isosceles triangle (a) has two sides of length 5 and base 6, isosceles triangle (b) has two sides of length 8 and base 6, and isosceles triangle (c) has two sides of length 10 and base 6. Which statement about their heights is true?
  5. In the sequence 100,94,82,64,40,...100, 94, 82, 64, 40, ... what is the pattern, and what comes next?
  6. In the sequence 3,7,15,31,63,…3, 7, 15, 31, 63, \ldots, what is the 88th term?
  7. In a tournament, teams are eliminated when they lose. If there are 127 teams initially and each game eliminates exactly one team, how many total games must be played to determine the champion?
  8. Compare the values: (A) 38×169\frac{3}{8} \times \frac{16}{9} and (B) 25×158\frac{2}{5} \times \frac{15}{8}
  9. The sequence 9,18,36,72,144,...9, 18, 36, 72, 144, ... follows a clear multiplication rule. What is the 8th term?
  10. Compare the quantities: (a) 910−25\frac{9}{10} - \frac{2}{5} and (b) 12\frac{1}{2}
  11. In the sequence 1,5,14,30,55,91,...1, 5, 14, 30, 55, 91, ... what pattern emerges, and what is the next term?
  12. The sequence 4,7,13,25,49,...4, 7, 13, 25, 49, ... follows a specific rule. What is the 6th term?
  13. What is the missing term in the sequence: 1,4,13,40,‾,364,10931, 4, 13, 40, \underline{\hspace{2em}}, 364, 1093?
  14. Compare the values: (a)(a) (34)3×6427\left(\frac{3}{4}\right)^3 \times \frac{64}{27} and (b)(b) 169×(34)2\frac{16}{9} \times \left(\frac{3}{4}\right)^2
  15. What is the 1212th term in the sequence: 1,1,2,3,5,8,13,21,…1, 1, 2, 3, 5, 8, 13, 21, \ldots where each term after the second is the sum of the two preceding terms?
  16. 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?
  17. Twice the smallest of three consecutive integers is 14 more than the largest. What is the middle integer?
  18. The sequence 1,1,2,3,5,8,13,...1, 1, 2, 3, 5, 8, 13, ... continues according to its established rule. What is the 10th term?
  19. The sequence 2,5,11,23,47,...2, 5, 11, 23, 47, ... follows a specific rule. What is the 6th term?
  20. Compare the quantities: (a) 13+16\frac{1}{3} + \frac{1}{6} and (b) 12\frac{1}{2}

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