Nursing Elites

1. Solve for x: 3(x - 1) = 2(3x - 9)

• A. x = 2
• B. x = 8/3
• C. x = -5
• D. x = 5

Correct answer: D

Rationale: To solve the equation 3(x - 1) = 2(3x - 9), first distribute and simplify both sides to get 3x - 3 = 6x - 18. Next, subtract 3x from both sides to get -3 = 3x - 18. Then, add 18 to both sides to obtain 15 = 3x. Finally, divide by 3 to find x = 5. Therefore, the correct answer is x = 5. Choices A, B, and C are incorrect because they do not represent the correct solution to the given equation after proper algebraic manipulation.

2. Which is bigger, a mile or a kilometer? What's the conversion factor?

• A. Mile is bigger; 1 mile is 1.609 km
• B. Kilometer is bigger; 1 km is 1.609 miles
• C. Mile is bigger; 1 mile is 1.5 km
• D. Kilometer is bigger; 1 km is 2 miles

Correct answer: A

Rationale: A mile is bigger than a kilometer. The correct conversion factor is 1 mile = 1.609 km. This means that one mile is equivalent to approximately 1.609 kilometers. Choice B is incorrect because a mile is bigger than a kilometer, and the conversion is not 1 km = 1.609 miles. Choice C is incorrect as the conversion factor provided is inaccurate; 1 mile is not equal to 1.5 km. Choice D is incorrect as it states that a kilometer is bigger, which is not true according to the actual conversion factor.

3. To begin making her soup, Jennifer added four containers of chicken broth with 1 liter of water into the pot. Each container of chicken broth contains 410 milliliters. How much liquid is in the pot?

• A. 1.64 liters
• B. 2.64 liters
• C. 5.44 liters
• D. 6.12 liters

Correct answer: B

Rationale: Each container of chicken broth contains 410 milliliters. Jennifer added four containers, which totals 4 * 410 = 1640 milliliters of chicken broth. She then added 1 liter of water, equivalent to 1000 milliliters. Combining all the liquids, we get 1640 + 1000 = 2640 milliliters, which equals 2.64 liters. Choice A is incorrect because it miscalculates the total liquid volume. Choice C is incorrect as it greatly overestimates the liquid amount. Choice D is incorrect as it also overestimates the liquid content in the pot.

4. Given that three vertices of a parallelogram are (1, 2), (3, 4), and (5, 6), what are the coordinates of the fourth vertex?

• A. (1, 6)
• B. (3, 2)
• C. (5, 2)
• D. (7, 8)

Correct answer: D

Rationale: To find the fourth vertex of a parallelogram, we can use the properties of a parallelogram. Opposite sides of a parallelogram are parallel and equal in length. Therefore, we can determine the fourth vertex by extending the line formed by the first two points. If we extend the line from (1, 2) to (3, 4), we find that it has a slope of 1. This means that extending the line from (3, 4) by the same slope will give us the fourth vertex. By adding 2 units to both x and y coordinates of (5, 6), we get (7, 8) as the coordinates of the fourth vertex. Therefore, the correct answer is (7, 8). Choices A, B, and C are incorrect as they do not satisfy the properties of a parallelogram and the given coordinate points.

5. Solve the equation 3(2x+5)=11x+5 for x. Which of the following is correct?

• A. 1
• B. 2
• C. -1
• D. -2

Correct answer: B

Rationale: To solve the equation, distribute 3 to both terms inside the parentheses: 6x + 15 = 11x + 5. Then, move 11x to the left side by subtracting it from both sides: 6x - 11x = 5 - 15. Simplify to get -5x = -10. Divide by -5 to isolate x: x = 2. Therefore, the correct answer is x = 2. Choices A, C, and D are incorrect because they do not match the correct solution obtained by solving the equation step by step.

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