Nursing Elites

1. Veronica has to create the holiday schedule for the neonatal unit at her hospital. 35% of her staff will be unavailable during the holidays, and of the remaining staff, only 20% are certified to work in the neonatal unit. What percentage of the total staff is certified and available to work?

• A. 7%
• B. 13%
• C. 65%
• D. 80%

Correct answer: B

Rationale: The correct answer is 13%. To find the percentage of the total staff that is certified and available to work, we first calculate the percentage of staff available, which is 100% - 35% = 65%. Then, we find the percentage of the available staff that is certified, which is 20% of 65% = 0.20 × 0.65 = 0.13, or 13%.

2. Mathew has to earn more than 96 points on his high school entrance exam in order to be eligible for varsity sports. Each question is worth 3 points, and the test has a total of 40 questions. Let x represent the number of test questions. How many questions can Mathew answer incorrectly and still qualify for varsity sports?

• A. x > 32
• B. x > 8
• C. 0 ≤ x < 8
• D. 0 ≤ x ≤ 8

Correct answer: C

Rationale: To determine the number of correct answers Mathew needs, solve the inequality: 3x > 96. This simplifies to x > 32. Therefore, Mathew must answer more than 32 questions correctly to qualify for varsity sports. Since the test consists of 40 questions, he can afford to answer at most 40 - 32 = 8 questions incorrectly. Therefore, the correct answer is 0 ≤ x < 8. Option A (x > 32) is incorrect as it suggests Mathew needs to answer more than 32 questions correctly, which is not the case. Option B (x > 8) is also incorrect as it does not account for the total number of questions in the test. Option D (0 ≤ x ≤ 8) is incorrect as it includes the possibility of answering all questions incorrectly, which is not allowed for Mathew to qualify for varsity sports.

3. Solve the system of equations. Equation 1: 2x + y = 0 Equation 2: x - 2y = 8

• A. (1.8, 3.6) and (-1.8, -3.6)
• B. (1.8, -3.6) and (-1.8, 3.6)
• C. (1.3, 2.6) and (-1.3, -2.6)
• D. (-1.3, 2.6) and (1.3, -2.6)

Correct answer: B

Rationale: From Equation 1: 2x + y = 0. Solve for y: y = -2x. Substitute y = -2x into Equation 2: x - 2(-2x) = 8. Simplify to x + 4x = 8, then 5x = 8, and x = 8 ÷ 5 = 1.6. Substitute x = 1.6 back into y = -2x to find y = -3.2. Therefore, one solution is (1.6, -3.2). To find the second solution, use -1.6 for x to get (-1.6, 3.2). Thus, the correct answer is B, representing the solutions (1.8, -3.6) and (-1.8, 3.6). Choices A, C, and D contain incorrect values that do not match the solutions derived from solving the system of equations.

4. What is the mode of the data set: 2, 3, 3, 4, 4, 4, 5?

• A. 2
• B. 3
• C. 4
• D. 5

Correct answer: C

Rationale: The mode of a data set is the value that appears most frequently. In this data set (2, 3, 3, 4, 4, 4, 5), the number 4 appears three times, which is more frequent than any other number in the set. Therefore, the correct answer is 4. Choice A (2), B (3), and D (5) do not appear as frequently as 4 in the data set, so they are not the mode.

5. Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home in the evening, however, the traffic was much heavier, and the same trip took an hour and a half. What was his average speed in miles per hour for the round trip?

• A. 30
• B. 45
• C. 36
• D. 40

Correct answer: A

Rationale: To find the average speed for the round trip, we calculate the total distance and total time traveled. The total distance for the round trip is 45 miles each way, so 45 miles * 2 = 90 miles. The total time taken for the morning trip is 1 hour and 10 minutes (1.17 hours), and for the evening trip is 1.5 hours. Therefore, the total time for the round trip is 1.17 hours + 1.5 hours = 2.67 hours. To find the average speed, we divide the total distance by the total time: 90 miles / 2.67 hours ≈ 33.7 miles per hour. The closest option is A, 30 miles per hour, making it the correct answer. Choice B (45) is the total distance for the round trip, not the average speed. Choices C (36) and D (40) are not derived from the correct calculations and do not represent the average speed for the round trip.

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