Nursing Elites

1. Simplify the following expression: 5/9 × 15/36

• A. 5/36
• B. 8/27
• C. 10/17
• D. 15/27

Correct answer: A

Rationale: To simplify the given expression, multiply the numerators together and the denominators together. 5/9 × 15/36 = (5 × 15) / (9 × 36) = 75 / 324. Now, simplify the resulting fraction by finding the greatest common divisor (GCD) of 75 and 324, which is 3. Divide both the numerator and denominator by 3 to get the simplified fraction: 75 ÷ 3 / 324 ÷ 3 = 25 / 108. Therefore, the simplified form of 5/9 × 15/36 is 25/108, which is equivalent to 5/36. Choice A, 5/36, is the correct answer. Choice B, 8/27, is incorrect as it does not match the simplified form of the expression. Choice C, 10/17, is unrelated and does not result from the given multiplication. Choice D, 15/27, does not correspond to the simplification of the given expression.

2. How can you visually differentiate between a histogram and a bar graph?

• A. A bar graph has gaps between the bars; a histogram does not
• B. A bar graph displays frequency; a histogram does not
• C. A histogram illustrates comparison; a bar graph does not
• D. A bar graph includes labels; a histogram does not

Correct answer: A

Rationale: The key difference between a histogram and a bar graph is that a bar graph has gaps between the bars, while a histogram does not. This feature helps in visually distinguishing between the two. Choice B is incorrect because both types of graphs can show frequency. Choice C is incorrect as both graphs can be used for comparison. Choice D is incorrect as both types of graphs can have labels for better understanding.

3. Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.

• A. 207.64
• B. 415.27
• C. 519.08
• D. 726.73

Correct answer: B

Rationale: The area of a circle is given by the formula A = π × r², where r is the radius. Since only half of the garden needs weeding, we calculate half the area. Using the given value of π (3.14) and a radius of 11.5 feet: A = 0.5 × 3.14 × (11.5)² A = 0.5 × 3.14 × 132.25 A = 0.5 × 415.27 A = 207.64 square feet. Thus, the area that needs weeding is approximately 207.64 square feet, making option B the correct answer. Choice A (207.64) is incorrect as it represents the total area of the circular garden, not just half of it. Choice C (519.08) and Choice D (726.73) are also incorrect as they do not reflect the correct calculation for finding the area of half the circular garden.

4. Which of the following equations does not represent a function?

• A. y = x^2
• B. y = sqrt(x)
• C. x = y^2
• D. y = 2x + 1

Correct answer: C

Rationale: An equation represents a function if each input (x-value) corresponds to exactly one output (y-value). In the equation x = y^2, for a single x-value, there are two possible y-values (positive and negative square root), violating the definition of a function. This violates the vertical line test, where a vertical line intersects the graph in more than one point for non-functions. Choices A, B, and D all pass the vertical line test and represent functions, making them incorrect answers.

5. Robert plans to drive 1,800 miles. His car gets 30 miles per gallon, and his tank holds 12 gallons. How many tanks of gas will he need for the trip?

• A. 4 tanks
• B. 5 tanks
• C. 6 tanks
• D. 7 tanks

Correct answer: B

Rationale: To calculate how many gallons of gas Robert needs for the 1,800-mile trip, divide the total distance by the car's mileage per gallon: 1,800 miles ÷ 30 mpg = 60 gallons. Since his tank holds 12 gallons, Robert will need 60 gallons ÷ 12 gallons per tank = 5 tanks of gas for the trip. Choice A (4 tanks), Choice C (6 tanks), and Choice D (7 tanks) are incorrect as they do not correctly calculate the number of tanks needed based on the car's mileage and tank capacity.

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