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. Adrian measures the circumference of a circular picture frame with a radius of 3 inches. Which of the following is the best estimate for the circumference of the frame?

• A. 12 inches
• B. 16 inches
• C. 18 inches
• D. 24 inches

Correct answer: C

Rationale: To calculate the circumference of a circle, use the formula 2πr, where r is the radius. In this case, with a radius of 3 inches, the estimated circumference would be 2 x π x 3 = 6π ≈ 18.85 inches. Therefore, the best estimate for the circumference of the frame is 18 inches (Choice C). Choice A (12 inches) is too small as it corresponds to the diameter rather than the circumference. Choice B (16 inches) and Choice D (24 inches) are also incorrect as they do not reflect the accurate calculation based on the given radius.

3. 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.

4. What is the formula to find the circumference of a circle?

• A. Circumference = 2πr
• B. Circumference = πr²
• C. Circumference = 2r²
• D. Circumference = r²π

Correct answer: A

Rationale: The correct formula to find the circumference of a circle is C = 2πr, where C represents the circumference and r is the radius of the circle. Choice B, Circumference = πr², represents the formula for the area of a circle rather than the circumference. Choice C, Circumference = 2r², is incorrect as it does not involve π in the formula. Choice D, Circumference = r²π, has the terms reversed compared to the correct formula; the formula should start with the constant (2) multiplied by π, followed by the radius.

5. Jonathan pays a $65 monthly flat rate for his cell phone. He is charged $0.12 per minute for each minute used in a roaming area. Which of the following expressions represents his monthly bill for x roaming minutes?

• A. 65 + 0.12x
• B. 65x + 0.12
• C. 65.12x
• D. 65 + 0.12x

Correct answer: A

Rationale: The correct expression for Jonathan's monthly bill is 65 + 0.12x, where x represents the number of roaming minutes. The $65 monthly flat rate is added to the product of $0.12 per minute and the number of roaming minutes (x). Choice B is incorrect because it incorrectly multiplies the flat rate by x and adds the per-minute charge. Choice C is incorrect as it combines the flat rate and the per-minute charge into a single value. Choice D is incorrect as it incorrectly multiplies the flat rate by x and adds the per-minute charge separately.

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