Practice Test 6 - ISEE Middle Level Quantitative Reasoning

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

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1. In science class, you roll two fair dice; what is the probability of sum 7?
2. A jar contains only dimes and quarters. Let d be the number of dimes. The number of quarters is 3 more than twice the number of dimes. Which expression represents the total value of the coins in the jar, in cents?
3. The average of three numbers, a, b, and c, is 16. Number b is twice number a. Number c is 8 more than number b. What is the value of number a?
4. In a class game, you roll two fair dice; what is the probability of sum 7?​
5. The average of a list of 5 numbers is 18. If one of the numbers in the list, 10, is removed and replaced with the number 30, what is the new average of the list?
6. A student has $b$ dollars and buys 5 pens for $p$ dollars each. How can the remaining balance be expressed algebraically?
7. A fair six-sided die is rolled and a spinner with four equal sections (Red, Blue, Green, Yellow) is spun. What is the probability that the die shows a prime number and the spinner does not land on Green?
8. Maya withdrew some money from her bank account. She spent $35 on a shirt. Then she gave half of the remaining money to her brother. If she has $40 left, how much money did she withdraw from her account originally?
9. A map has a scale where 2 inches represents 70 miles. The distance between two cities on this map is 5 inches. What is the actual distance between the two cities?
10. A race car travels at a constant speed of 120 miles per hour. How many feet does the car travel in one second? (Note: 1 mile = 5,280 feet)
11. The temperature of a chemical reaction starts at x degrees Celsius and increases by d degrees every minute for m minutes. The final Celsius temperature is then converted to Fahrenheit using the formula $F = \frac{9}{5}C + 32$. Which expression represents the final temperature in Fahrenheit?
12. A sequence of numbers starts with 1, 2, 4, 7, 11, 16, ... . The pattern continues. What is the rule to find the next number in the sequence?
13. A science experiment requires 250 milliliters of a solution every 6 hours. How many liters of the solution will be required for one full week?
14. The number of calories $B$ a person burns during a workout is estimated by the formula $B = 12w + 8r$, where $w$ is the number of minutes spent walking and $r$ is the number of minutes spent running. If a person only walks, what does the variable $w$ represent?
15. A family phone plan costs $90 per month for the first two lines. For each additional line, the cost is $15. The family uses n lines, where n is greater than 2. Which expression represents the total monthly cost for the lines?
16. The original price of a jacket is p dollars. It is on sale for 30% off. A sales tax of 7% is then applied to the discounted price. Which expression represents the final cost of the jacket?
17. A numerical sequence follows an alternating two-step rule. The sequence begins 2, 6, 3, 9, 6, 18, 15, ... If the pattern continues, what is the next number in the sequence?
18. Leo can assemble a bookshelf in 4 hours. Maria can assemble the same bookshelf in 6 hours. If they work together at their constant individual rates, how many minutes will it take them to assemble one bookshelf?
19. A standard soup can has a capacity of 10 fluid ounces. A restaurant chef makes a batch of soup that fills a pot with a capacity of 4 gallons. How many full cans of soup can be filled from this batch? (Note: 1 gallon = 128 fluid ounces)
20. A library charges a fine of $0.25 per day for an overdue book. For a book that is more than 10 days overdue, there is an additional flat fee of $5.00. If a book is returned 18 days overdue, what is the total fine?

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