Practice Test 2 - DAT Quantitative Reasoning

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

In a dental clinic, the ratio of disposable gloves used by the hygienists to those used by the dentists is $5:3$ . If the clinic ordered 640 pairs of gloves for hygienists this month, how many pairs were ordered for dentists, assuming the same ratio is maintained?
The table below shows the grade distributions from two sections of a statistics class. Refer to the table above to answer the question. What is the weighted mean grade across both sections combined?
A dental practice budgets $\$2{,}200$ – $\$2{,}800$ for software; which is the solution set for $2200\le 150x+850\le 2800$ ?
A radioactive isotope decays at 12\% per hour. If the initial mass is 250 mg, approximately how much remains after 3 hours? (Use $N=N_0(1-r)^t$ .)
Two machines produce identical items. Machine X produces items with weights normally distributed around 500g with standard deviation 10g. Machine Y produces items with weights normally distributed around 500g with standard deviation 15g. If one item each is randomly selected from both machines, what is the standard deviation of the difference in their weights?
A dental laboratory technician mixes three different alloys to create a crown material. Alloy A is 15% gold, Alloy B is 40% gold, and Alloy C is 65% gold. If she uses 20 grams of Alloy A, 30 grams of Alloy B, and some amount of Alloy C to create a mixture that is exactly 45% gold, how many grams of Alloy C must she use?
A dental student must pass $4$ independent practical exams, each with a $0.8$ probability of passing. What is the probability that the student passes exactly $3$ out of the $4$ exams?
The table below shows the cost and caloric content of four lunch options at a cafeteria. Based on the table, which option provides the lowest cost per 100 calories?
In a dental practice, the ratio of pediatric to adult to geriatric patients is 3:7:2. After a community outreach program, the ratio changes to 5:6:4. If the absolute value of the change in the number of adult patients is 45, and the total number of patients increases, what was the original total number of patients?
An orthodontic order contained small and large brackets in a ratio of 3 : 5. If 360 brackets were ordered in total, how many were large?
Investment Returns: Option A invests $\$2{,}000$ at $8\%$ simple interest for 1 year. Option B invests $\$3{,}200$ at $5\%$ simple interest for 1 year. 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.
The weekly number of patients seen by a dentist over 6 consecutive weeks was $18,\ 21,\ 24,\ 19,\ 27,\ 21$ . What was the mean number of patients per week?
Given that $\alpha$ and $\beta$ are angles in the first quadrant with $\sin \alpha = \frac{3}{5}$ and $\cos \beta = \frac{5}{13}$ , compare the quantities: Quantity A: $\cos \alpha + \sin \beta$ Quantity B: $\frac{17}{13}$
Find the set of $x$ that satisfies both $x+5>2$ and $3x-1<8$ .
If $x$ and $y$ are positive real numbers with $x^2 + y^2 = 25$ and $xy = 12$ , compare the quantities: Quantity A: $x + y$ Quantity B: $|x - y|$
A medical device has a $2\%$ failure rate. If $10$ such devices are used independently, what is the probability that exactly $2$ devices fail?
The histogram shows the distribution of test scores for 25 students in four score ranges: 60-70, 70-80, 80-90, and 90-100. Based on the histogram, which of the following best approximates the mean score?
A dental laboratory has three technicians working on crown fabrication. Technician A completes a crown in 2.5 hours, Technician B in 3 hours, and Technician C in 4 hours. If they receive an order for 15 crowns and all three work simultaneously until completion, how long will it take to complete the entire order?
If $|2x - 5| + |x + 1| = 8$ , what is the sum of all possible values of $x$ ?
Solve the inequality $x^{2}-5x+4<0$ .

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