Practice Test 7 - DAT Quantitative Reasoning

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

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1. A culture from dental plaque triples every day; if $N(t)=80\cdot3^t$, what is $N(2)$ after $2$ days?
2. A medical research study involves testing a new dental treatment on patients. The probability that a patient responds positively to Treatment A is $0.6$, to Treatment B is $0.4$, and to both treatments is $0.25$. If a patient is selected at random and responds positively to Treatment A, what is the probability that this patient also responds positively to Treatment B?
3. A pharmaceutical company mixes three compounds in a ratio such that compound A comprises 25% of the mixture, the ratio of compound B to compound C is 5:7, and the absolute difference between the actual percentage of compound C and 43.75% is minimized. If the total mixture is 800 mL, what is the volume of compound B in mL?
4. A dentist drives from her office to a dental conference at an average speed of 55 mph. On the return trip, construction delays reduce her average speed to 35 mph. If the total driving time for the round trip is 5.4 hours, what is the distance between her office and the conference location?
5. A periodontal practice tracks treatment success rates. For patients under 40, the success rate is 92%. For patients 40-60, it's 87%. For patients over 60, it's 78%. This month, they treated 25 patients under 40, 35 patients aged 40-60, and 15 patients over 60. If the practice needs an overall success rate of at least 86% to maintain their certification, do they meet this requirement, and by what margin?
6. After a 25% markup and a 20% discount on the new price, an item sells for $90. What was the original price?
7. Market Analysis: Company A's initial profit is $\$90{,}000$ with projected growth of $10\%$. Company B's initial profit is $\$75{,}000$ with projected growth of $20\%$. 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.
8. Distance Traveled: Route A is $210$ km at $70$ km/h. Route B is $180$ km at $60$ km/h. Quantity A is the travel time for Route A, and Quantity B is the travel time for Route B. Determine whether Quantity A is greater, Quantity B is greater, or both are equal.
9. The solutions of $2x^2-7x-4=0$ are
10. Investment Returns: Option A invests $\$12{,}000$ at $3\%$ simple interest for 4 years. Option B invests $\$9{,}000$ at $4\%$ simple interest for 4 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.
11. A dental practice implements a referral bonus system. For each new patient referral, the referring patient receives a credit equal to 15% of the new patient's first-year revenue. The practice tracks that referred patients generate an average of $850 in their first year, while walk-in patients generate $720. If 35% of new patients are referrals and the practice gains 240 new patients annually, what is the total amount paid out in referral bonuses per year?
12. The dot plot shows the number of patients seen per day at a clinic over 10 days. Based on the dot plot, what is the difference between the mean and the mode?
13. The table below shows results of testing 200 patients for a disease. What is the probability that a patient actually has the disease given that they tested positive?
14. Two dental laboratories independently produce crowns with defect rates of $5\%$ and $8\%$ respectively. If one crown is randomly selected from each laboratory, what is the probability that at least one crown is defective?
15. A bag contains $8$ red marbles, $6$ blue marbles, and $4$ green marbles. Three marbles are drawn consecutively without replacement. What is the probability that the first marble is red, the second is blue, and the third is green?
16. Solve $9^{x}=27$.
17. Use the Venn diagram shown. A student is chosen at random from a class of 50. What is the probability that the student takes Chemistry but NOT Biology, given that the student takes at least one of the two subjects?
18. A boat travels 15 miles downstream and then returns upstream over the same distance. The river's current is 2 mph, and the boat's speed in still water is 10 mph. How many hours does the round trip take?
19. The time $T$ required to polish a denture set varies inversely with the number of technicians $n$. If 2 technicians can finish in 45 minutes, how long will 5 technicians take, working at the same rate?
20. Solve for $x$: $7(2x-3)-4(1-x)=2x+5$

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