Nursing Elites

1. Solve for x: 4(2x - 6) = 10x - 6

• A. x = 5
• B. x = -7
• C. x = -9
• D. x = 10

Correct answer: C

Rationale: To solve the equation 4(2x - 6) = 10x - 6, first distribute 4 into the parentheses: 8x - 24 = 10x - 6. Next, simplify the equation by rearranging terms: 8x - 10x = -6 + 24, which gives -2x = 18. Solving for x by dividing by -2 on both sides gives x = -9. Therefore, the correct answer is x = -9. Choice A (x = 5), Choice B (x = -7), and Choice D (x = 10) are incorrect solutions obtained by errors in solving the equation.

2. Which of the following is equivalent to 3.28?

• A. (328/100)
• B. (41/5)
• C. (3/28)
• D. (7/25)

Correct answer: D

Rationale: To convert a decimal to a fraction, we can treat it as a fraction over 1 and then simplify. For 3.28, it can be written as 3.28/1. To convert this to a fraction, we multiply by 100 to get (328/100). Then, to simplify, we divide both the numerator and denominator by 4 to get (82/25). This simplifies further to (7/25). Therefore, (7/25) is equivalent to 3.28. Choices A, B, and C are incorrect as they do not represent the decimal 3.28.

3. What is the surface area of the cylinder shown below?

• A. 602.9 cm²
• B. 904.3 cm²
• C. 1,408.7 cm²
• D. 1,507.2 cm²

Correct answer: D

Rationale: The surface area of a cylinder can be calculated using the formula: S = 2πr² + 2πrh, where r is the radius and h is the height. Substituting the values for radius (12) and height (8) into the formula: S = 2π(12)² + 2π(12)(8). S = 2π(144) + 2π(96). S = 288π + 192π. S = 480π ≈ 1507.964. Therefore, the surface area of the cylinder is approximately 1507.2 square centimeters. Choice A, 602.9 cm², is incorrect as it is significantly lower than the correct value. Choice B, 904.3 cm², is also incorrect as it does not match the calculated surface area. Choice C, 1,408.7 cm², is incorrect as it does not align with the calculated value of the surface area.

4. Melissa is ordering fencing to enclose a square area of 5625 square feet. How many feet of fencing does she need?

• A. 75 feet
• B. 150 feet
• C. 300 feet
• D. 5,625 feet

Correct answer: C

Rationale: To find the side length of the square, we take the square root of the area: √5625 ft² = 75 ft. The perimeter of a square is 4 times its side length, so the fencing needed is 4 × 75 ft = 300 ft. Therefore, Melissa needs 300 feet of fencing to enclose the square area of 5625 square feet. Option A (75 feet) is the side length of the square, not the fencing needed. Option B (150 feet) is half of the correct answer and does not account for all sides of the square. Option D (5,625 feet) is the total area, not the length of fencing required.

5. A dry cleaner charges $3 per shirt, $6 per pair of pants, and an extra $5 per item for mending. Annie drops off 5 shirts and 4 pairs of pants, 2 of which need mending. Assuming the cleaner charges an 8% sales tax, what will be the amount of Annie’s total bill?

• A. $45.08
• B. $49.00
• C. $52.92
• D. $88.20

Correct answer: C

Rationale: To determine the total cost before tax, calculate: 5 shirts × $3/shirt + 4 pants × $6/pair of pants + 2 items mended × $5/item mended = $49. Now, multiply this amount by 1.08 to include the 8% sales tax: $49 × 1.08 = $52.92. Therefore, Annie's total bill will be $52.92. Choice A, $45.08, is incorrect as it does not include the correct calculation for the total bill. Choice B, $49.00, is wrong because it is the total cost before tax and does not consider the added sales tax. Choice D, $88.20, is incorrect as it does not accurately calculate the total bill including the sales tax.

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