Practice Test 4 - SSAT Upper Level Quantitative

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

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1. A factory produces widgets at a rate of 150 widgets per hour. Due to a machine malfunction, the production rate decreases by 20% for 3 hours, then returns to normal. If the factory operates for 8 hours total, how many widgets are produced?
2. A sequence is defined by $a_1 = 2$, $a_2 = 5$, and $a_n = 3a_{n-1} - 2a_{n-2}$ for $n \geq 3$. Which term first exceeds $100$?
3. If $x$ satisfies $\frac{x}{4} + \frac{x}{12} = \frac{x}{6} - 4$, then $\frac{2x}{3}$ equals:
4. A parking garage charges $3 for the first hour and $1.50 for each additional hour or part thereof. If someone parks for 4 hours and 20 minutes, and then receives a 15% discount for being a frequent customer, what is the final parking fee?
5. Two water pumps are being tested. Pump X can fill a 1,200-gallon tank in 40 minutes, while Pump Y can fill a 1,800-gallon tank in 45 minutes. If both pumps work together to fill a 3,000-gallon tank, approximately how long will it take?
6. A car travels 180 miles in 3 hours. For the first hour, it travels at 50 mph. For the remaining distance, it maintains a constant speed. What is this constant speed for the last two hours?
7. A printing company charges $0.08 per page for the first 500 pages and $0.06 per page for each additional page. A copying service charges a flat rate of $0.07 per page regardless of quantity. For what number of pages do both services cost exactly the same amount?
8. The sum of two prime numbers is 30. If one of the primes is greater than 20, how many such pairs of primes are possible?
9. A parking garage charges $3 for the first hour and $1.50 for each additional hour or fraction thereof. If someone parks for more than one hour, which expression correctly represents the total cost for parking $h$ hours, where $h > 1$?
10. Consider the sequence $2, 6, 18, 54, 162, \ldots$ and the sequence $1, 5, 25, 125, 625, \ldots$. If the $n$th terms of these sequences are added together, what type of sequence is formed?
11. Which of the following statements about the number 91 is true?
12. A cone and a cylinder have the same base radius $r$ and the same height $h$. If the volume of the cylinder is 216 cubic units, what is the volume of the cone?
13. A model train is built to a scale of $1:87$. If the model locomotive is $6.2$ inches long, and the real locomotive travels $280$ miles in $4$ hours $40$ minutes, what is the speed of the real locomotive in miles per hour?
14. A recipe that serves $6$ people calls for $2\frac{1}{4}$ cups of flour. If you want to serve $14$ people but only have $4\frac{3}{4}$ cups of flour available, what is the maximum number of people you can actually serve with the flour you have?
15. A student converts $\frac{7}{12}$ to a percentage and rounds to the nearest tenth of a percent. What percentage does the student report?
16. At a store, rank these discounts from smallest to largest value: $\frac{1}{5}$, $0.18$, $15\%$, $\frac{3}{16}$, $0.22$.
17. A number $N$ has exactly 6 positive divisors. If $N = 2^a \cdot 3^b$ where $a$ and $b$ are non-negative integers, and $N > 12$, what is the smallest possible value of $N$?
18. The value $\frac{7}{11}$ lies between which pair of benchmark percentages?
19. A company produces widgets at a cost of $3.50 each, plus a daily fixed cost of $200 for equipment. If the company sells each widget for $7.25 and produces and sells $x$ widgets in a day, which expression represents the daily profit?
20. A sequence follows the pattern where each term is the sum of the two preceding terms, similar to the Fibonacci sequence. If the first term is $x$, the second term is $x + 3$, and the fifth term is $34$, what is the value of the third term?

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