Practice Test 6 - 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. Consider the sequence where each term is the average of the two preceding terms: $12, 8, 10, 9, 9.5, 9.25, \ldots$ If this pattern continues indefinitely, what value does the sequence approach?
2. A recipe for trail mix calls for nuts, dried fruit, and chocolate chips in the ratio $3:2:1$. If Sarah wants to use all $1.2$ pounds of chocolate chips she has, how many pounds of nuts should she use to maintain the proper ratio?
3. For a prime $n$ greater than 3, which expression can never be prime?
4. A number is $25\%$ larger than $\frac{4}{5}$. Which expression represents this number?
5. A car's fuel efficiency is rated at 35 miles per gallon. If gasoline costs $4.20 per gallon, what is the cost per mile to operate this vehicle, expressed in cents?
6. A weather station records that 2.8 inches of rain fell during a storm. If this rain were collected over a flat roof area of 1,500 square feet, how many gallons of water would be collected? (1 cubic foot = 7.48 gallons)
7. A car rental company charges a base fee plus a mileage charge. The total cost for renting a car for one day and driving $m$ miles is $C = 45 + 0.25m$ dollars. If a customer's total bill was $78.50, which equation could be used to find the number of miles driven?
8. In a basketball league, teams earn 3 points for a win, 1 point for a tie, and 0 points for a loss. If a team has played $g$ games and has $w$ wins and $t$ ties, which expression represents the number of losses?
9. Store A sells oranges at 5 pounds for $4.25, while Store B sells oranges at 8 pounds for $6.40. Store C sells oranges at 3 pounds for $2.70. Which store offers the best price per pound, and by how much does it beat the most expensive option?
10. If $p$ and $q$ are integers such that $\frac{p}{q} = 0.\overline{36}$, what is the value of $p + q$ when the fraction is in lowest terms?
11. Three real numbers $r$, $s$, and $t$ satisfy the following conditions: $r < s < t$, $r + s + t = 0$, and $rst = \frac{1}{8}$. If $r = -\frac{1}{2}$, which of the following represents the correct ordering of $|r|$, $|s|$, and $|t|$ from least to greatest?
12. A rectangular garden has length that is 8 feet more than twice its width. If the width is $w$ feet, and the gardener wants to install a fence around the entire perimeter plus an additional gate that costs the same as 5 feet of fencing, which expression represents the total feet of fencing needed?
13. A contractor estimates that $8$ workers can complete a job in $15$ days. After $6$ days, $2$ workers are reassigned to another project. Assuming all workers work at the same rate, how many additional days will it take the remaining workers to finish the job?
14. A spherical balloon has a radius of 9 inches. If the radius is decreased by $\frac{1}{3}$ of its length, the original volume is how many times the new volume?
15. If $a = 2^3$ and $b = 2^4$, what is the value of $\frac{a^2 \cdot b^3}{(ab)^2}$?
16. The ratio of the ages of three siblings is $2:3:5$. In $4$ years, their ages will be in the ratio $3:4:6$. What is the current age of the youngest sibling?
17. A recipe calls for ingredients to be mixed at a rate of 2 cups per 3 minutes. If a chef mixes for 15 minutes but takes a 2-minute break after every 5 minutes of mixing, what is the total amount mixed?
18. If $4-3(2x-1)=13$, what is $x$?
19. A water tank in the shape of a right circular cone (vertex pointing down) has a radius of 12 feet at the top and a height of 16 feet. When the tank is filled to a depth of 8 feet from the vertex, what is the volume of water in the tank?
20. Maria's salary increased by $12\%$ and then by another $8\%$. What single percent increase would have the same effect as these two consecutive increases?

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