Practice Test 5 - 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. Which expression has the greatest value?
2. In a survey, $0.375$ of respondents preferred coffee, $\frac{2}{5}$ preferred tea, and the remaining $22.5\%$ preferred other beverages. What fraction of coffee and tea drinkers combined preferred coffee?
3. Two parallel lines are cut by two different transversals. The first transversal creates an angle of $58°$ with the first parallel line. The second transversal creates corresponding angles, one of which is $3x + 14°$ and another which is $5x - 22°$. What is the value of $x$?
4. In quadrilateral $PQRS$, the sum of three angles is $285°$. If angle $P$ is twice angle $Q$, and angle $R$ equals angle $Q$ plus $15°$, what is the measure of angle $S$?
5. In a sequence, the first term is $3$, and each subsequent term is obtained by multiplying the previous term by $2$ and then subtracting $1$. What is the difference between the 5th term and the 4th term?
6. What is the least integer greater than -7/4?
7. In a science lab, which recorded value is the greatest: $0.62$, $\frac{5}{8}$, $61\%$, $0.59$, or $\frac{3}{5}$?
8. If $a = -\frac{5}{8}$, $b = -0.62$, and $c = -\frac{3}{5}$, which of the following correctly orders these three numbers from least to greatest?
9. A delivery service charges $2.50 for the first mile and $1.75 for each additional mile. A competitor charges $1.90 per mile for any distance. At what distance do both services charge exactly the same amount, and what is that amount?
10. A geometric sequence has its 3rd term equal to $18$ and its 6th term equal to $486$. If all terms are positive, what is the 4th term?
11. An isosceles triangle has two equal sides of length 13 cm and a base of length 10 cm. What is the area of the triangle?
12. Which of the following is equivalent to $\left(\frac{2^3}{2^{-1}}\right)^2 \div 2^4$?
13. The mean of 8 numbers is 15. If two numbers, 12 and 18, are removed from the set, what is the mean of the remaining 6 numbers?
14. A store marks up the wholesale cost of an item by $40\%$ to set the retail price, then offers a $25\%$ discount during a sale. If the sale price is $63, what was the wholesale cost?
15. The number of students in a school increased by $15\%$ from Year 1 to Year 2, then decreased by $10\%$ from Year 2 to Year 3. If there were $1,242$ students in Year 3, how many students were there in Year 1?
16. A store offers a discount that reduces the original price by $\frac{2}{9}$. If this is equivalent to a $22.\overline{2}\%$ discount, what can you conclude?
17. If 8 is subtracted from 3 times a number, the result is 4 more than twice the number. Find it.
18. For which value of $k$ is $(2^k)^3 \cdot 2^{-5} = \frac{1}{4}$?
19. If $n$ is a positive integer such that $n^2 + n + 41$ is composite, what is the smallest possible value of $n$?
20. If $x$ and $y$ satisfy the system $\begin{cases} 2x + 3y = 12 \\ x - y = 1 \end{cases}$, then $xy$ equals:

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