Nursing Elites

1. If 𝑛 = 8, then n is between which of the following ranges?

• A. 5 and 7
• B. 7 and 9
• C. 9 and 11
• D. 3 and 5

Correct answer: B

Rationale: To find the range where n lies when n = 8, we consider numbers greater and lesser than 8. The range would be between 7 and 9, not 9 and 11 as stated in the original rationale. Option A (5 and 7) and Option D (3 and 5) are lower ranges, while Option C (9 and 11) exceeds the upper limit.

2. 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.

3. What is the area of the largest circle that can fit entirely inside a rectangle that measures 8 centimeters by 10 centimeters?

• A. 18π cm²
• B. 10π cm²
• C. 16π cm²
• D. 8π cm²

Correct answer: C

Rationale: The largest circle that can fit inside the rectangle would have a diameter of 8 cm, which means the radius is half of the diameter, thus 4 cm. The area of a circle is calculated using the formula A = πr², where r is the radius. Substituting the radius value into the formula, the area of the circle is π(4)² = 16π cm². Therefore, the correct answer is 16π cm². Choice A (18π cm²), B (10π cm²), and D (8π cm²) are incorrect because they do not represent the area of the largest circle that fits inside the given rectangle.

4. 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.

5. 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.

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