Nursing Elites

1. Simplify the expression. Which of the following is the value of x? (5(4x – 5) = (3/2)(2x – 6))

• A. −(2/7)
• B. −(4/17)
• C. (16/17)
• D. (8/7)

Correct answer: C

Rationale: To solve the given proportion 5(4x – 5) = (3/2)(2x – 6), first distribute to get 20x - 25 = 3x - 9. Then, simplify the linear equation by isolating x: 20x - 3x = 25 - 9, which leads to 17x = 16. Finally, solving for x gives x = 16/17. Choice A is incorrect as it does not match the calculated value of x. Choice B is incorrect as it does not correspond to the correct solution for x. Choice D is incorrect as it does not align with the accurate value of x obtained from solving the equation.

2. Simplify the expression: 2x + 3x - 5.

• A. 5x - 5
• B. 5x
• C. x - 5
• D. 2x - 5

Correct answer: A

Rationale: To simplify the expression 2𝑥 + 3𝑥 - 5, follow these steps: Identify and combine like terms. The terms 2𝑥 and 3𝑥 are both 'like terms' because they both contain the variable 𝑥. Add the coefficients of the like terms: 2𝑥 + 3𝑥 = 5𝑥. Simplify the expression. After combining the like terms, the expression becomes 5𝑥 - 5, which includes the simplified term 5𝑥 and the constant -5. Thus, the fully simplified expression is 5𝑥 - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

3. Curtis measured the temperature of water in a flask in his science class. The temperature of the water was 35 °C. He carefully heated the flask so that the temperature of the water increased by about 2 °C every 3 minutes. Approximately how much had the temperature of the water increased after 20 minutes?

• A. 10 °C
• B. 13 °C
• C. 15 °C
• D. 35 °C

Correct answer: B

Rationale: To find the increase in temperature after 20 minutes, calculate how many 3-minute intervals are in 20 minutes (20 ÷ 3 = 6.66, rounding to 7 intervals). Then, multiply the temperature increase per interval (2 °C) by the number of intervals (7 intervals), giving a total increase of 14 °C. Therefore, after 20 minutes, the temperature of the water would have increased by approximately 14 °C. Choice A, 10 °C, is incorrect as it underestimates the total increase. Choice C, 15 °C, is incorrect as it overestimates the total increase. Choice D, 35 °C, is incorrect as it represents the initial temperature of the water, not the increase in temperature.

4. The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be correct for the lengths of the other two sides of the triangle? (Note: A² + B² = C²)

• A. 5 inches, 12 inches
• B. 2.5 inches, 6 inches
• C. 2.5 inches, 4 inches
• D. 5 inches, 8 inches

Correct answer: A

Rationale: The correct answer is A. Using the Pythagorean theorem (A² + B² = C²), we substitute the values: 5² + 12² = 13². This simplifies to 25 + 144 = 169, which is true. Therefore, 5 inches and 12 inches could be the lengths of the other two sides. Choices B, C, and D do not satisfy the Pythagorean theorem, making them incorrect options.

5. In the problem 6 + 3 × 2, which operation should be completed first?

• A. Multiplication
• B. Addition
• C. Division
• D. Subtraction

Correct answer: A

Rationale: The correct answer is 'Multiplication.' According to the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), multiplication should be completed first. In the given expression, 3 × 2 should be solved before adding 6 to the result. This means that the multiplication operation should be prioritized over addition. Choices B, C, and D are incorrect because, in the order of operations, multiplication takes precedence over addition, division, and subtraction, respectively.

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