Nursing Elites

1. What are all the factors of 12?

• A. 12, 24, 36
• B. 1, 2, 4, 6, 12
• C. 12, 24, 36, 48
• D. 1, 2, 3, 4, 6, 12

Correct answer: D

Rationale: The factors of 12 are numbers that divide evenly into 12 without leaving a remainder. The correct factors of 12 are 1, 2, 3, 4, 6, and 12. Choice A (12, 24, 36) is incorrect as only 12 is a factor of 12. Choice B (1, 2, 4, 6, 12) includes all the correct factors of 12. Choice C (12, 24, 36, 48) is incorrect as 24, 36, and 48 are not factors of 12.

2. John’s Gym charges its members according to the equation y = 40x, where x is the number of months and y represents the total cost to each customer after x months. Ralph’s Recreation Room charges its members according to the equation y = 45x. What relationship can be determined about the monthly cost to the members of each company?

• A. John’s monthly membership fee is equal to Ralph’s monthly membership fee.
• B. John’s monthly membership fee is more than Ralph’s monthly membership fee.
• C. John’s monthly membership fee is less than Ralph’s monthly membership fee.
• D. No relationship can be determined between the monthly membership fees.

Correct answer: C

Rationale: The equation y = 40x represents John's Gym charging $40 per month, while the equation y = 45x represents Ralph's Recreation Room charging $45 per month. Since $40 is less than $45, it can be concluded that John's Gym offers a lower monthly membership fee compared to Ralph's Recreation Room. Therefore, the correct answer is that John’s monthly membership fee is less than Ralph’s monthly membership fee. Choices A and B are incorrect because John's fee is not equal to or greater than Ralph's fee. Choice D is incorrect as there is a clear relationship indicating that John’s monthly membership fee is less than Ralph’s monthly membership fee.

3. 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.

4. Simplify (x^2 - y^2) / (x - y)

• A. x + y
• B. x - y
• C. 1
• D. (x + y)/(x - y)

Correct answer: A

Rationale: The expression 𝑥^2 - 𝑦^2 is a difference of squares, which follows the identity: 𝑥^2 - 𝑦^2 = (𝑥 + 𝑦)(𝑥 - 𝑦). Therefore, the given expression becomes: (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) = (𝑥 + 𝑦)(𝑥 - 𝑦) / (𝑥 - 𝑦). Since (𝑥 - 𝑦) appears in both the numerator and the denominator, they cancel each other out, leaving 𝑥 + 𝑦. Thus, the simplified form of (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) is 𝑥 + 𝑦. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.

5. The total perimeter of a rectangle is 36 cm. If the length of each side is 12 cm, what is the width?

• A. 3 cm
• B. 12 cm
• C. 6 cm
• D. 8 cm

Correct answer: C

Rationale: The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Given that the total perimeter is 36 cm and each side's length is 12 cm, we substitute the values into the formula: 36 = 2(12 + w). Solving for w gives us w = 6. Therefore, the width of the rectangle is 6 cm. Choice A (3 cm) is incorrect because the width is not half of the length. Choice B (12 cm) is the length, not the width. Choice D (8 cm) is incorrect as it does not match the calculated width of 6 cm.

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