Practice Test 6 - ISEE Upper Level Quantitative Reasoning

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

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1. A car's value $V$ (in dollars) after $t$ years of ownership is modeled by $V = 25000(0.85)^t$. After 3 years, what does the expression $(0.85)^3$ represent in this depreciation model?
2. A survey found that 60% of people like chocolate, 70% like vanilla, and 40% like both chocolate and vanilla. If a person is selected at random, what is the probability that they like chocolate but not vanilla?
3. Consider the alternating sequence: 1, -4, 9, -16, 25, -36, ... What is the 11th term?
4. For a baking recipe, Priya needed 16 oz of sugar but wanted grams for her metric scale. She used $1\text{ oz}=28.35\text{ g}$ and calculated $\text{g}=\text{oz}\times28.35$. How many grams was 16 oz, rounded to the nearest gram?
5. A delivery truck travels at an average speed of 40 mph in the city and 65 mph on the highway. If the truck spends 75% of its time on the highway during a 4-hour trip, what is the total distance traveled?
6. A store sells 4 pencils for $1.20. At this same rate, how much would 15 pencils cost?
7. The temperature $T$ (in degrees Fahrenheit) in a freezer $m$ minutes after a power outage begins is modeled by $T = -5 + 2m$. What does the coefficient 2 indicate about the freezer's temperature?
8. A company's profit $P$ (in thousands of dollars) is related to the number of units sold $n$ by the equation $P = 12n - 200$. What does it mean when $P = 0$ in this business context?
9. The fraction $\frac{7}{12}$ is between which two consecutive percentages?
10. A gear with 20 teeth is connected to a gear with 35 teeth. If the smaller gear makes 42 rotations, how many rotations does the larger gear make?
11. A garden adds 9 plants per row: $14, 23, 32, 41, 50$; calculate the 10th term.
12. An investment ledger shows $80, 92, 104, 116, 128$ dollars; which option completes the sequence correctly?
13. Two dice are rolled simultaneously. What is the probability that their sum is greater than 8, given that both dice show even numbers?
14. A bacteria culture doubles every $3$ hours. If there are initially $N$ bacteria, which expression represents the number of bacteria after $3t$ hours?
15. A plant grows 2 cm each week from 10 cm. How would the output height change if input weeks increases by 4?​​
16. A bag contains 8 red marbles and 12 blue marbles. Two marbles are drawn without replacement. What is the probability that the first marble is red and the second marble is blue?
17. A bookstore orders 144 books at $15 each. They receive a 20% trade discount but must pay 8% sales tax on the discounted price. What is the total amount paid?
18. A car uses 3 gallons of gas to travel 84 miles. How many gallons will it need to travel 210 miles at the same rate?
19. A quality control inspector finds that $\frac{3}{8}$ of products from Machine A, $37.6\%$ of products from Machine B, and $0.374$ of products from Machine C meet specifications. Which machine has the highest rate of products meeting specifications?
20. Based on the recipe ratios shown in the table, if a baker uses 6 cups of flour for whole wheat bread, how many cups of water should be used?

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