Nursing Elites

1. A homeowner has hired two people to mow his lawn. If person A is able to mow the lawn in 2 hours by herself and person B is able to mow the lawn in 3 hours by himself, what is the amount of time it would take for both person A and B to mow the lawn together?

• A. 5 hours
• B. 2.5 hours
• C. 1.2 hours
• D. 1 hour

Correct answer: C

Rationale: To find the combined work rate, you add the individual work rates: 1/2 + 1/3 = 5/6. This means that together, they can mow 5/6 of the lawn per hour. To determine how long it would take for both A and B to mow the entire lawn, you take the reciprocal of 5/6, which gives you 6/5 or 1.2 hours. Therefore, it would take 1.2 hours for person A and person B to mow the lawn together. Choice A (5 hours) is incorrect because it does not consider the combined efficiency of both workers. Choice B (2.5 hours) is incorrect as it does not reflect the correct calculation based on the combined work rates of the two individuals. Choice D (1 hour) is incorrect as it doesn't consider the fact that the combined rate is less than the individual rate of person A alone, thus taking longer than 1 hour.

2. On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 50 cm². What is the actual area of the room?

• A. 500 m²
• B. 50 m²
• C. 5000 cm²
• D. 500 cm²

Correct answer: D

Rationale: The scale of 1:100 means that 1 cm² on the floor plan represents 100 cm² in real life. To find the actual area of the room, you need to multiply the area on the floor plan by the square of the scale factor. Since the scale is 1:100, the scale factor is 100. Therefore, 50 cm² on the floor plan represents 50 * 100 = 5000 cm² in real life. Choice A (500 m²) is incorrect as it converts the area from cm² to m² without considering the scale factor. Choice B (50 m²) is incorrect as it does not account for the scale factor. Choice C (5000 cm²) is incorrect as it gives the area on the floor plan, not the actual area.

3. A piece of wood that is 7 1/2 feet long has 3 1/4 feet cut off. How many feet of wood remain?

• A. 4 1/4 feet
• B. 4 1/2 feet
• C. 3 1/2 feet
• D. 3 3/4 feet

Correct answer: A

Rationale: To find the remaining length of wood, you need to subtract 3 1/4 feet from 7 1/2 feet. When you subtract the fractions, 7 1/2 - 3 1/4, you get 15/2 - 13/4 = 30/4 - 13/4 = 17/4 = 4 1/4 feet. Therefore, the correct answer is 4 1/4 feet. Choice B (4 1/2 feet) is incorrect because the subtraction result is not 1/2. Choice C (3 1/2 feet) is incorrect as it does not match the correct result of 4 1/4 feet. Choice D (3 3/4 feet) is also incorrect as it does not align with the correct answer obtained from the subtraction of fractions.

4. What defines rational and irrational numbers?

• A. Any number that can be expressed as a fraction; any number that cannot be expressed as a fraction
• B. Any number that terminates or repeats; any number that does not terminate or repeat
• C. Any whole number; any decimal
• D. Any terminating decimal; any repeating decimal

Correct answer: A

Rationale: Rational numbers are those that can be written as a simple fraction, including whole numbers and decimals that either terminate or repeat. Irrational numbers, on the other hand, cannot be expressed as fractions. Choice B is incorrect because not all rational numbers necessarily terminate or repeat. Choice C is incorrect as it oversimplifies the concept of rational and irrational numbers by only considering whole numbers and decimals. Choice D is incorrect as it inaccurately defines rational and irrational numbers solely based on decimals terminating or repeating, excluding the broader category of fractions.

5. Which of the following is the correct decimal placement for the product of 1.6 * 0.93?

• A. 14.88
• B. 0.1488
• C. 1.488
• D. 0.001488

Correct answer: C

Rationale: To find the product of 1.6 * 0.93, you multiply these two numbers to get 1.488. Therefore, the correct decimal placement for the product is 1.488. Choice A, 14.88, is incorrect as it incorrectly places the decimal two spots to the right. Choice B, 0.1488, is incorrect as it incorrectly places the decimal one spot to the right. Choice D, 0.001488, is incorrect as it incorrectly places the decimal three spots to the right.

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