Practice Test 3 - DAT Quantitative Reasoning

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

Start practice test

1. Population Growth: City A starts with $300{,}000$ people and grows by $3\%$ per year. City B starts with $330{,}000$ 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.
2. Solve for $x$: $3^{2x-1}=27$.
3. A dental lab charges $120 setup plus $15 per crown; if total is $345, solve $120+15x=345$ for $x$.
4. In a clinical trial, $60\%$ of patients respond to Treatment A, $40\%$ respond to Treatment B, and $25\%$ respond to both. If a patient responds to at least one treatment, what is the probability that the patient responds to Treatment A?
5. A 500 g alloy contains 18\% silver. How many grams of pure silver must be added so that the new alloy is 20\% silver?
6. Refer to the deck configuration shown. From a specially prepared 20-card deck (shown below), two cards are drawn without replacement. What is the probability that exactly one of the two cards is a 'Star' card?
7. Refer to the two urns shown below. A coin is flipped: if heads, a ball is drawn from Urn A; if tails, from Urn B. Given that a red ball was drawn, what is the probability that it came from Urn A?
8. What is the least integer $n$ such that $2^{n}>1000$?
9. A hygiene kit costs $25 plus $3 per disposable item; if total is $55, solve $25+3x=55$ for $x$.
10. For $a > 0$ and $b > 0$ with $a \neq b$, compare the quantities: Quantity A: $\frac{a^4 + b^4}{a^2 + b^2}$ Quantity B: $\frac{(a^2 + b^2)^2}{2(a^2 + b^2)}$
11. A single fair die is rolled twice. What is the probability that the sum of the two rolls is at least 10?
12. A dental practice schedules $5$ appointments per day. Each patient has a $15\%$ probability of canceling independently. What is the probability that exactly $1$ patient cancels?
13. Solve $|x+1|\le4$.
14. Based on the trend line in the scatter plot below, which of the following best describes the correlation between age and amount spent on dental care?
15. How many liters of 25\% acid must be mixed with 15 L of 60\% acid to produce a solution that is 40\% acid?
16. The scatter plot shows the relationship between hours of study (x) and exam scores (y) for 10 students, along with the line of best fit. Based on the scatter plot, how many data points lie strictly above the line of best fit by more than 5 points on the y-axis?
17. The variance of a data set with values $x_1, x_2, x_3, x_4, x_5$ is 16. What is the variance of the data set with values $2x_1 + 3, 2x_2 + 3, 2x_3 + 3, 2x_4 + 3, 2x_5 + 3$?
18. An assistant's wage rose from $18.50 to $20.35 per hour. What is the percent increase, to the nearest tenth of a percent?
19. What is the solution set of $4^{3-x}\geq 16^{2x}$?
20. The heights of students in a class have mean 68 inches and variance 16 square inches. If heights are converted to centimeters using the conversion 1 inch = 2.54 cm, what is the new variance in square centimeters?

Practice tests