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. Mom's car drove 72 miles in 90 minutes. How fast did she drive in feet per second?

• A. 0.8 feet per second
• B. 48.9 feet per second
• C. 0.009 feet per second
• D. 70.4 feet per second

Correct answer: B

Rationale: To convert miles per hour to feet per second, you need to convert miles to feet and minutes to seconds. First, convert 72 miles to feet using the conversion factor 1 mile = 5280 feet: 72 miles * 5280 feet/mile = 380160 feet. Then, convert 90 minutes to seconds: 90 minutes * 60 seconds/minute = 5400 seconds. Now, to find the speed in feet per second, divide the distance traveled in feet by the time in seconds: 380160 feet / 5400 seconds = 70.4 feet per second. Therefore, the correct answer is 70.4 feet per second. Choice A, 0.8 feet per second, is incorrect as it is a much lower speed. Choice C, 0.009 feet per second, is also incorrect as it is too low. Choice D, 70.4 feet per second, would be correct if the conversion calculations were accurate, but in this case, it's not the correct answer.

3. Out of 9 trips, a person chooses the longest route for 3 of them. What percentage of their trips is the longest route?

• A. 0.25
• B. 0.33
• C. 0.5
• D. 0.75

Correct answer: B

Rationale: To find the percentage of trips where the person chose the longest route, divide the number of longest route trips (3) by the total number of trips (9) and multiply by 100. This gives (3/9) * 100 = 33.33%, which can be rounded to 33%. Therefore, the correct answer is B. Choice A (0.25), C (0.5), and D (0.75) are incorrect because they do not accurately represent the percentage of trips where the longest route was chosen based on the given information.

4. Tom needs to buy ink cartridges and printer paper. Each ink cartridge costs $30. Each ream of paper costs $5. He has $100 to spend. Which of the following inequalities may be used to find the combinations of ink cartridges and printer paper he may purchase?

• A. 30c + 5p ≤ 100
• B. 30c + 5p = 100
• C. 30c + 5p > 100
• D. 30c + 5p < 100

Correct answer: A

Rationale: The correct inequality is 30c + 5p ≤ 100. This represents the combinations of ink cartridges (c) and printer paper (p) that Tom may purchase, ensuring the total cost is less than or equal to $100. Choice B is incorrect because the total cost should be less than or equal to $100, not equal to. Choices C and D are also incorrect as they indicate the total cost being greater than $100, which is not the case given Tom's budget limit.

5. At the beginning of the day, Xavier has 20 apples. At lunch, he meets his sister Emma and gives her half of his apples. After lunch, he stops by his neighbor Jim’s house and gives him 6 of his apples. He then uses ¾ of his remaining apples to make an apple pie for dessert at dinner. At the end of the day, how many apples does Xavier have left?

• A. 4
• B. 6
• C. 2
• D. 1

Correct answer: D

Rationale: Xavier starts with 20 apples. He gives half of his apples to his sister Emma, which is 20 ÷ 2 = 10 apples, leaving him with 10 apples. Then, he gives 6 apples to his neighbor Jim, leaving him with 10 - 6 = 4 apples. Using ¾ of his remaining 4 apples for the pie, he uses 3/4 x 4 = 3 apples. Therefore, he has 4 - 3 = 1 apple left at the end of the day. Choice D, 1 apple, is the correct answer. Choices A, B, and C are incorrect because Xavier ends up with 1 apple remaining, not 4, 6, or 2.

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