Practice Test 4 - DAT Quantitative Reasoning

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

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1. The table below shows the distribution of blood types among 400 donors at a blood drive. Based on the table, if one donor is selected at random, what is the probability that the donor is either Rh-negative OR has type AB blood (or both)?
2. Find the sum of all real solutions of $2^{2x}-6(2^x)+8=0$.
3. A researcher collects data on exam scores from two classes. Class A has 15 students with a mean score of 82 and standard deviation of 6. Class B has 25 students with a mean score of 78 and standard deviation of 8. What is the overall mean score for all 40 students combined?
4. A dentist has 8 different colored polishing cups and will select 3 of them and arrange them in order on a bracket. How many different ordered arrangements are possible?
5. Accepted to rejected ratio is 5:3. If 240 more are accepted than rejected, how many applied?
6. A drawer contains 6 blue masks and 4 white masks. Two masks are randomly selected without replacement. What is the probability that at least one mask is white?
7. A bag has 3 red, 4 blue, and 5 green marbles. Drawing 3 without replacement, what is P(all different colors)?
8. A pipe fills a tank in 6 h; another fills it in 12 h. A drain empties it in 8 h. All open, how many hours to fill it?
9. A dental tray is 32 cm long. Approximately how many inches is this, using $1\text{ in}=2.54\text{ cm}$?
10. The box-and-whisker plot summarizes the blood-pressure readings for 40 patients. Using the plot shown, what is the interquartile range (IQR), and approximately what percentage of the readings fall between 118 and 142?
11. Find all real numbers $x$ satisfying $|2x-7|=3$.
12. Bacteria on a dental impression doubles every hour; if $N(t)=150\cdot2^t$, what does it predict for $t=4$ hours?
13. Dr. Lee invests $\$10{,}000$ at 3\% simple annual interest. How much interest will accumulate in 2 years and 3 months?
14. A dentist mixes $x$ mL of fluoride concentrate at $0.40/mL plus $5 bottle cost; if total is $21, solve $0.40x+5=21$ for $x$.
15. During a sale, the price of a curing light decreased by 15\% and later increased by 10\%. If the final price was $561, what was the original price before the sale?
16. A password consists of 3 different consonant letters followed by 2 distinct digits (0–9). All consonants and digits may be used at most once. If order matters in both parts, how many different passwords are possible?
17. The bar graph shows the number of cavities found in 5 classrooms of students. Based on the graph shown, if one additional classroom with an unknown number of cavities x is added, for what value of x will the mean of all 6 classrooms equal the median of all 6 classrooms?
18. The probability distribution table for discrete random variable X is shown. What is $P(X \geq 3 \mid X \geq 2)$?
19. Refer to the grid shown below. A particle starts at point A (lower-left) and moves to point B (upper-right) by taking unit steps only right or up. If each valid path is equally likely, what is the probability that the particle passes through point C?
20. If $P(A)=0.4,P(B)=0.5$, and $P(A|B)=0.2$, what is $P(A\cup B)$?

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