Practice Test 6 - DAT Quantitative Reasoning

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

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1. Solve for $x$: $-3(2-x)>9$
2. Three dental assistants can prepare 60 instrument kits in 4 hours. At the same rate, how many hours will it take 5 assistants to prepare 150 kits?
3. Population Growth: City A has $200{,}000$ people and grows by $4\%$ per year. City B has $240{,}000$ people and grows by $2\%$ per year. After 1 year, Quantity A is City A's population and Quantity B is City B's population. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
4. If $5^{x+1}=125^{\;2-x}$, then $x$ equals
5. Population Growth: City A starts at $500{,}000$ and grows by $1\%$ per year. City B starts at $450{,}000$ and grows by $2\%$ per year. After 1 year, Quantity A is City A's population and Quantity B is City B's population. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
6. The stacked bar chart below shows the number of patients (in hundreds) seen at a clinic each weekday, broken down by type of visit. Refer to the chart. What percentage of all Emergency visits for the week occurred on Wednesday and Thursday combined?
7. Use the bar chart to answer the question. What fraction of Orthodontics revenue came from the North region?
8. If $2^{x+1} + 2^{x+2} + 2^{x+3} = 112$, what is the value of $x$?
9. A dental practice has two hygienists working simultaneously. Sarah can clean teeth at a rate that would complete all appointments for the day in 8 hours working alone. Michael can complete the same workload in 12 hours working alone. If they work together for 3 hours, then Sarah works alone for the remaining time, how many total hours does it take to complete all appointments?
10. For what values of $k$ does the system of equations $2x + 3y = 7$ and $kx + 6y = 14$ have infinitely many solutions?
11. A dental clinic has a $95\%$ success rate for root canals. If $6$ independent root canal procedures are performed, what is the probability that exactly $5$ are successful?
12. The system $\begin{cases}y=x+1\\y=x^{2}-3\end{cases}$ is satisfied by which set of $x$-coordinates?
13. Given $a > 1$ and $b > 1$, compare the quantities: Quantity A: $\log_a(b) + \log_b(a)$ Quantity B: $2$
14. The line graph shows the population of bacteria (in millions) in a culture over 6 hours. Based on the line graph shown, during which one-hour interval was the average rate of change in population greatest in magnitude?
15. A 250 mL bottle of mouth rinse is 12\% active ingredient. How many milliliters of water must be added to dilute the solution to 9\% active ingredient?
16. Compare the quantities: Quantity A: $\frac{3^{15} \cdot 5^{12}}{3^{13} \cdot 5^{10}}$ Quantity B: $\frac{2^8 \cdot 7^6}{2^6 \cdot 7^4}$
17. For $x > 0$, compare the quantities: Quantity A: $\sqrt{x^2 + 16x + 64}$ Quantity B: $x + 8$
18. Population Growth: City A has $800{,}000$ people and grows by $1.5\%$ per year. City B has $760{,}000$ people and grows by $2\%$ per year. After 1 year, Quantity A is City A's population and Quantity B is City B's population. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
19. Solve the inequality $\dfrac{5-2x}{3}\le x+1$.
20. A new dental office budgets $\$4{,}000$ to $\$5{,}200$ for chairs; which represents $4000\le 800x+800\le 5200$ solution set?

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