Nursing Elites

1. Which of the following equations does not represent a function?

• A. y = x^2
• B. y = sqrt(x)
• C. x = y^2
• D. y = 2x + 1

Correct answer: C

Rationale: An equation represents a function if each input (x-value) corresponds to exactly one output (y-value). In the equation x = y^2, for a single x-value, there are two possible y-values (positive and negative square root), violating the definition of a function. This violates the vertical line test, where a vertical line intersects the graph in more than one point for non-functions. Choices A, B, and D all pass the vertical line test and represent functions, making them incorrect answers.

2. In a fraction, which number is the numerator and which is the denominator?

• A. Numerator: top, Denominator: bottom
• B. Numerator: bottom, Denominator: top
• C. Numerator: left, Denominator: right
• D. Numerator: right, Denominator: left

Correct answer: A

Rationale: The correct answer is A: 'Numerator: top, Denominator: bottom.' In a fraction, the numerator is the top number, representing the part of the whole being considered, while the denominator is the bottom number, indicating the total number of equal parts into which the whole is divided. Choices B, C, and D are incorrect because they provide inaccurate descriptions of the numerator and denominator positions in a fraction.

3. What defines a composite number?

• A. A number with only two factors
• B. A number that is a fraction
• C. A number with more than 2 factors
• D. A number with exactly two factors

Correct answer: C

Rationale: A composite number is a positive integer greater than one that has more than two factors. Choice A is incorrect because a number with only two factors is a prime number. Choice B is incorrect as being a fraction does not define a composite number. Choice D is incorrect because a number with exactly two factors is a prime number, not a composite number.

4. Solve for x in the equation: 3x - 5 = 16

• A. 7
• B. 5
• C. 8
• D. 9

Correct answer: C

Rationale: To solve for x, add 5 to both sides of the equation: 3x - 5 + 5 = 16 + 5, which simplifies to 3x = 21. Next, divide both sides by 3: x = 21 ÷ 3 = 7. Therefore, the correct answer is x = 7, making option A the correct choice. Option C, '8,' is incorrect as it is not the solution obtained from the correct calculations. Options B and D, '5' and '9,' are also incorrect and not the solution to the given equation.

5. Simplify the expression. Which of the following is correct? (3/2)(8/3) ÷ (5/4)

• A. 1
• B. 2
• C. 3
• D. 4

Correct answer: B

Rationale: Using PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction): (3/2)(8/3) ÷ (5/4) = (24/6) ÷ (5/4) = (4/1) ÷ (5/4). To divide fractions, the second fraction is flipped and then multiplied by the first fraction, resulting in (4/1)(4/5) = (16/5), which simplifies to 3(1/5) or 2.

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