Practice Test 3 - 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 swimming pool is being filled with water. In the first hour, 120 gallons are added. In each subsequent hour, 25% more water is added than in the previous hour. How many gallons are added in the fourth hour?
2. A garden sprinkler waters a circular area with a radius of 8.4 feet. If a rectangular lawn is 28 feet by 15 feet, approximately what percentage of the lawn can be watered by placing the sprinkler at the center?
3. A bank offers €0.85 per $1; how many euros will you receive for $240?
4. A construction worker estimates that laying 850 bricks will take 6 hours. After 2.5 hours, he has laid 320 bricks. At this rate, will he finish on time, and by approximately how much?
5. In a data set of 12 values, the median is 45 and the range is 30. If 5 is added to each value, what will be the new median and new range, respectively?
6. A recursive sequence is defined by $a_1 = 5$ and $a_{n+1} = a_n + 2n + 2$ for $n ≥ 1$. What is $a_4$?
7. The equation $ax + 6 = 4x - 2$ has no solution when $a$ equals which value?
8. In a chess tournament, the ratio of wins to losses to draws for Player A is $4:1:2$. Player A has played 21 games total. If Player A wins the next 3 games, what will be the new ratio of wins to total games played?
9. A machine produces widgets at a rate such that the number of widgets $N$ after $h$ hours follows $N = 120h - 5h^2$. What does the term $-5h^2$ most likely represent in this production model?
10. A store gives 10% off a $50 item. If input is discount rate, output is final price, what is the output?​​
11. In an arithmetic sequence, the first term is 7 and the common difference is -3. Which term in the sequence is equal to -20?
12. A water tank is filled by two pipes. Pipe A fills the tank at 15 gallons per minute, and Pipe B fills at 10 gallons per minute. If Pipe A operates for the first 20 minutes alone, then both pipes operate together for the next 15 minutes, how many gallons are added to the tank?
13. Two angles are complementary. If one angle is 3 times the measure of the other, what is the measure of the larger angle?
14. Two congruent isosceles triangles each have a base of 10 units and base angles of 65°. If these triangles are positioned so their bases overlap completely, what is the measure of the vertex angle in each triangle?
15. A factory produces 1,440 widgets per day. Each widget requires 3 bolts, and bolts are sold in packages of 24. If the factory operates 5 days per week, how many packages of bolts are needed for one week of production?
16. The decimal $0.024$ is what percent of $\frac{3}{5}$?
17. A factory produces red, blue, and green widgets in the ratio $6:4:5$. If production increases such that red widget output doubles, blue widget output increases by 50%, and green widget output remains constant, what is the new ratio of red to blue to green widgets?
18. A function $m(n)$ gives the number of minutes it takes to complete $n$ problems, where $m(n) = 3n + 5$. If it takes 26 minutes to complete a certain number of problems, how long would it take to complete twice as many problems?
19. A sequence begins with the terms 3, 7, 11, 15, 19, ... If this pattern continues, which expression gives the $n$th term of the sequence?
20. A meteorologist reports that the probability of rain is $\frac{7}{20}$ on Monday, $35.2\%$ on Tuesday, and $0.348$ on Wednesday. On which day is rain most likely?

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