Practice Test 1 - DAT Quantitative Reasoning

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

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1. Two dice are rolled simultaneously. Given that the sum is greater than $8$, what is the probability that both dice show the same number?
2. Solve for $x$: $\dfrac{x+2}{x-1}=2$, $x\ne1$.
3. A clinic budgets $600–$900 for masks; which is the solution set for $600\le 30x+120\le 900$?
4. A dental supply company bought a batch of instruments for $2,400 and plans to sell each instrument for $35. What is the minimum number of instruments that must be sold to realize a 25\% profit on the purchase cost?
5. A solution is 70\% water by volume. After 40 mL of water evaporates, the solution becomes 60\% water. What was the original volume of the solution?
6. The double bar graph compares the number of cavities found in two age groups across four different towns. Based on the graph, in which town is the ratio of Children's cavities to Adults' cavities closest to 3:5?
7. Investment Returns: Option A invests $\$10{,}000$ at $4\%$ simple interest for 5 years. Option B invests $\$8{,}000$ at $5\%$ simple interest for 5 years. Quantity A is the interest earned in Option A, and Quantity B is the interest earned in Option B. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
8. Market Analysis: Company A starts with $\$120{,}000$ profit and grows by $12\%$. Company B starts with $\$110{,}000$ profit and grows by $15\%$. Quantity A is Company A's projected profit after growth, and Quantity B is Company B's projected profit after growth. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
9. The frequency table below summarizes the number of dental visits per year for 20 patients. Using the table provided, what is the variance of the distribution?
10. For positive $k,kx^2+4x+1=0$ has one real solution. What is $k$?
11. Refer to the radar chart to answer the question. Which category shows the greatest difference between Clinic P and Clinic Q?
12. A fair coin is tossed until a head appears or until 3 tosses are made. What is the expected number of tosses?
13. A disinfectant-resistant strain grows by factor $1.1$ per hour; if $N(t)=900(1.1)^t$, what is $N(3)$?
14. The table shows the quarterly revenue (in thousands of dollars) for a dental practice over two years. Based on the table shown, which quarter exhibited the largest percentage increase in revenue compared to the same quarter of the previous year?
15. The cumulative frequency graph shows the distribution of exam scores for 200 students. Based on the cumulative frequency graph, approximately how many students scored between 60 and 80?
16. The table below gives the results of a random sample. Based on the data in the table, what is the sample standard deviation (use n−1 in the denominator)?
17. A dental laboratory charges a setup fee of $95 plus $40 per crown fabricated. If the bill for the month was $1,135, how many crowns were fabricated?
18. Population Growth: City A has $600{,}000$ people and grows by $2.5\%$ per year. City B has $615{,}000$ 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. The coordinate plane below shows the graphs of two functions f(x) and g(x). Based on the graphs shown, for how many integer values of x in the interval [−4, 4] is f(x) > g(x)?
20. The table below shows the weights (in kg) of samples A through E. Using the data in the table, if each weight is multiplied by 3 and then 5 is subtracted, what are the new mean and new standard deviation, respectively?

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