Nursing Elites

1. Jeremy put a heavy chalk mark on the tire of his bicycle. His bike tire is 27 inches in diameter. When he rolled the bike, the chalk left marks on the sidewalk. Which expression can be used to best determine the distance, in inches, the bike rolled from the first mark to the fourth mark?

• A. 3(27π)
• B. 4π(27)
• C. (27 ÷ 3)π
• D. (27 ÷ 4)π

Correct answer: A

Rationale: The distance traveled by the bike in one complete roll of the tire is equal to the circumference, which can be calculated using the formula C = πd, where d is the diameter. Given that the diameter of the bike tire is 27 inches, the circumference is obtained by multiplying the diameter by π. As the tire rolls from the first mark to the fourth mark, it completes three full rotations (one complete roll plus two more). Therefore, the total distance rolled is 3 times the circumference, which results in 3(27π). Choice A is correct. Choice B is incorrect as it incorrectly multiplies the diameter by 4π instead of multiplying the circumference by 4. Choices C and D are incorrect as they involve dividing the diameter by a number, which is not applicable in this context.

2. Four people split a bill. The first person pays 1/5, the second person pays 1/3, and the third person pays 1/12. What fraction of the bill does the fourth person pay?

• A. 1/4
• B. 13/60
• C. 47/60
• D. 1/4

Correct answer: C

Rationale: To find the fourth person's share, subtract the fractions paid by the first three people from the total bill (1). The first person pays 1/5, the second person pays 1/3, and the third person pays 1/12. Adding these fractions gives 7/15. Subtracting this from 1 gives the fourth person's share as 8/15, which simplifies to 4/5. Therefore, the fourth person pays 4/5 of the bill. Option A (1/4) is incorrect because it does not consider the fractions paid by the first three people. Option B (13/60) is incorrect as it is not the remainder after subtracting the first three fractions from 1. Option D (1/4) is a duplicate of Option A and is also incorrect.

3. 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.

4. Curtis is taking a road trip through Germany, where all distance signs are in metric. He passes a sign that states the city of Dusseldorf is 45 kilometers away. Approximately how far is this in miles?

• A. 42 miles
• B. 37 miles
• C. 28 miles
• D. 16 miles

Correct answer: C

Rationale: To convert kilometers to miles, you can use the conversion factor of approximately 0.62 miles per kilometer. Therefore, 45 kilometers × 0.62 miles/kilometer = 27.9 miles, which is approximately 28 miles away. Choice A (42 miles), Choice B (37 miles), and Choice D (16 miles) are incorrect as they do not reflect the accurate conversion from kilometers to miles.

5. A woman wants to stack two bookcases, one 32.75 inches tall and another 17.25 inches tall. How tall will they be when stacked together?

• A. 49.5 inches
• B. 50 inches
• C. 48 inches
• D. 51 inches

Correct answer: B

Rationale: To find the total height of the stacked bookcases, you need to add the heights of the two bookcases: 32.75 inches + 17.25 inches = 50 inches. Therefore, the correct answer is 50 inches. Choice A (49.5 inches) is incorrect as it does not consider rounding off the total height. Choices C (48 inches) and D (51 inches) are incorrect as they do not accurately calculate the sum of the heights of the two bookcases.

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