Practice Test 7 - 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 cylindrical water tank has a radius of 4.3 feet and height of 12.7 feet. Using the formula $V = \pi r^2 h$, which is the best estimate for the tank's volume?
2. A bakery sells muffins for $2.50 each and cookies for $1.25 each. On a particular day, they sell twice as many cookies as muffins. If they sell $m$ muffins, which expression represents their total revenue for that day?
3. The heights of 6 basketball players are 68, 70, 72, 74, 76, and 78 inches. A 7th player joins the team. If the new median height is 73 inches, what are the possible values for the 7th player's height?
4. The cost function $C(n) = 25n + 150$ gives the total cost (in dollars) to produce $n$ items. If the cost increased by $200 when production increased from $n$ items to $n + k$ items, what is the value of $k$?
5. In the figure, triangle ABC has angle A = 35° and angle B = 80°. Point D is on side BC such that AD bisects angle A. What is the measure of angle DAB?
6. A discount of $12.5\%$ reduces a price from $\$P$ to $42. What is $P$ expressed as a mixed number?
7. A rectangular piece of cardboard measuring 24 inches by 18 inches has squares cut from each corner. The sides are then folded up to create an open box. If each corner square has a side length of 3 inches, what is the volume of the resulting box?
8. A stock price drops 30% on Monday, rises 40% on Tuesday, and drops 25% on Wednesday. If the stock price at the end of Wednesday is $77.175, what was the price at the beginning of Monday?
9. A water tank contains 840 gallons. Water is being drained at 12 gallons per minute while simultaneously being filled at 7 gallons per minute. How long will it take to empty the tank completely?
10. A streaming service charges $8 monthly plus $2 per movie. Which output occurs when input movies equals 5?​​
11. The back-to-back stem-and-leaf plot compares test scores for two different teaching methods. What can be concluded about the effectiveness of the two methods?
12. One triangle has sides of length 5, 7, and 8, and a second triangle has sides of length 5, 7, and 8. Which statement about their congruence is correct?
13. A number decreased by 8 is equal to 3 times the sum of the number and 4. What is the number?
14. Using complementary angles, if $\triangle ABC$ is right at $C$ and $m\angle A=35^\circ$, find $m\angle B$.
15. A cooking recipe listed 12 oz of chocolate, but Amir wanted grams for his scale. He used $1\text{ oz}=28.35\text{ g}$ and wrote $\text{g}=\text{oz}\times28.35$. How many grams was 12 oz, rounded to the nearest gram?
16. A water tank contains 500 gallons initially. Water flows out at a rate of 15 gallons per hour. If $V$ represents the volume of water remaining after $t$ hours, what does the variable $t$ represent when $V = 200$?
17. On a blueprint, 1/4 inch represents 3 feet. If a room measures 2.5 inches long on the blueprint, what is the actual length of the room?
18. In a science experiment, the thermometer read $86^\circ\text{F}$, but the report required Celsius. The student used $C=(F-32)\times\frac{5}{9}$. What temperature in Celsius corresponded to $86^\circ\text{F}$?
19. The ratio of teachers to students at Lincoln School is 1:18. If there are 24 teachers, how many students are there?
20. A map scale is 1 inch to 10 feet; a hallway measures 3 feet, so how many inches on the map?

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