Practice Test 4 - 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 machine produces 150 widgets in 2.5 hours. At this rate, how many widgets can it produce in 7 hours?
2. A store marks up items by $33\frac{1}{3}\%$. If an item originally costs $24, what is the new price expressed as a decimal?
3. A soup recipe for 4 servings uses 2 cups broth; if 1 cup = 8 oz, how many ounces for 12 servings?
4. A rectangular prism has dimensions 6 cm by 8 cm by 10 cm. What is the total surface area of this prism?
5. A recipe called for 2.5 gallons of soup for a fundraiser, but the pot was marked in liters. The cook used $1\text{ gal}=3.785\text{ L}$ and wrote $\text{L}=\text{gal}\times3.785$. How many liters was 2.5 gal, rounded to one decimal place?
6. In an arithmetic sequence, the 3rd term is 14 and the 7th term is 26. What is the 15th term?
7. A rectangular prism has a square base with side length 5 inches and a height of 12 inches. A smaller rectangular prism with a square base of side length 3 inches and height 8 inches is removed from the center of the larger prism. What is the volume of the remaining solid?
8. A regular hexagon has a side length of 8 units. What is the area of the hexagon?
9. A water tank holds 500 liters when full. If water is being drained at a rate of 1.2 gallons per minute, how long will it take to empty the tank? (Note: 1 gallon ≈ 3.785 liters)
10. A mixture contains water and alcohol in the ratio $5:3$. If $12.5\%$ of the mixture is removed, what percent of the remaining mixture is water?
11. A theater budget is sets:costumes $=7:5$; if costumes increase $50\%$, what is the new ratio?
12. A rectangular prism has dimensions 12.4 cm × 7.8 cm × 5.2 cm. Using the formula $V = l \times w \times h$, which is the most reasonable estimate for the volume?
13. A recipe for trail mix calls for 3 cups of nuts for every 2 cups of dried fruit. If Maria wants to make a batch using 4.5 cups of nuts, how many cups of dried fruit should she use?
14. A cylindrical water tank has a radius of 4 feet and a height of 12 feet. If the tank is filled to 75% of its capacity, approximately how many cubic feet of water does it contain?
15. The number of employees at a company decreased by 18% due to layoffs, then increased by 25% due to new hires. If the final number of employees is 1,025, what was the original number of employees?
16. Jamie has 3 more than twice the number of stickers that Alex has. If Jamie has 17 stickers, how many stickers does Alex have?
17. The distance $D$ (in miles) between two cars initially 200 miles apart and driving toward each other is $D = 200 - 90t$, where $t$ is time in hours. What does the value of $t$ represent when $D = 20$?
18. A function $p(t)$ represents the profit (in dollars) from selling $t$ items, where $p(t) = 15t - 200$. How many items must be sold for the profit to equal $100?
19. A delivery truck travels at 45 mph for the first 2 hours of its route, then at 60 mph for the next 3 hours. What is the truck's average speed for the entire trip?
20. In a class, $40\%$ of students are boys. Of the boys, $\frac{3}{8}$ play soccer. What percent of the entire class consists of boys who play soccer?

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