Nursing Elites

1. 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.

2. What is the overall median of Dwayne's current scores: 78, 92, 83, 97?

• A. 19
• B. 85
• C. 83
• D. 87.5

Correct answer: B

Rationale: To find the median of a set of numbers, first arrange the scores in ascending order: 78, 83, 92, 97. Since there is an even number of scores, we find the median by taking the average of the two middle values. In this case, the middle values are 83 and 92. Calculating (83 + 92) / 2 = 85, we determine that the overall median of Dwayne's scores is 85. Choice A (19) is incorrect as it does not correspond to any value in the given set of scores. Choice C (83) is the median of the original set but not the overall median once arranged. Choice D (87.5) is the average of all scores but not the median.

3. What is 4.6 rounded to the nearest integer?

• A. 3
• B. 4
• C. 5
• D. 6

Correct answer: C

Rationale: When rounding a decimal number to the nearest integer, if the decimal part is 0.5 or greater, we round up to the next integer; if it is less than 0.5, we round down. In this case, 4.6 is closer to 5 than to 4 because it is exactly halfway between the two integers. Therefore, when rounding 4.6 to the nearest integer, we round up to 5. Choice A (3), B (4), and D (6) are incorrect as they are not the nearest integer to 4.6.

4. Which number is larger, 0.5 or 1/3?

• A. 0.5
• B. 1/3
• C. They are equal
• D. Cannot be determined

Correct answer: A

Rationale: To compare 0.5 and 1/3, we can convert 0.5 to a fraction, which is 1/2. When comparing 1/2 and 1/3, we find that 1/2 is greater than 1/3. Therefore, 0.5 is larger than 1/3. Choice B is incorrect as 1/3 is smaller. Choice C is incorrect as the numbers are not equal. Choice D is incorrect as a clear comparison can be made.

5. A patient requires a 20% decrease in medication dosage. Their current dosage is 400 mg. What will their dosage be after the decrease?

• A. 60 mg
• B. 80 mg
• C. 120 mg
• D. 320 mg

Correct answer: B

Rationale: To calculate a 20% decrease of 400 mg, you multiply 400 mg by 0.20 to get 80 mg. Subtracting 80 mg from the current dosage of 400 mg results in a new dosage of 320 mg. Choice A is incorrect because it miscalculates the decrease. Choice C is incorrect as it represents a 20% increase instead of a decrease. Choice D is incorrect as it represents the initial dosage, not the reduced dosage.

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