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. Between the years 2000 and 2010, the number of births in the town of Daneville increased from 1432 to 2219. What is the approximate percent increase in the number of births?

• A. 55%
• B. 36%
• C. 64%
• D. 42%

Correct answer: A

Rationale: To calculate the percent increase, subtract the initial value from the final value, which gives 2219 - 1432 = 787. Then, divide the increase (787) by the initial value (1432) and multiply by 100 to get the percentage: (787/1432) * 100 = 55%. Therefore, the approximate percent increase in the number of births is 55%. Choice B, 36%, is incorrect because it does not match the calculated increase. Choice C, 64%, is incorrect as it is higher than the actual percentage. Choice D, 42%, is incorrect as it is lower than the actual percentage.

3. If you have a rectangle with a width of 5 inches and a length of 10 inches and scale it by a factor of 2, what will the new perimeter be?

• A. 30 inches
• B. 40 inches
• C. 60 inches
• D. 50 inches

Correct answer: C

Rationale: When a rectangle is scaled by a factor of 2, both the length and width are multiplied by 2. The new dimensions become width = 5 * 2 = 10 inches and length = 10 * 2 = 20 inches. Therefore, the new perimeter is calculated as 2 * (10 + 20) = 60 inches. Choice A, B, and D are incorrect as they do not reflect the correct calculation based on scaling the dimensions of the rectangle.

4. If he pays $270 per month in rent, how much money does he put into his house savings account each month?

• A. $90
• B. $270
• C. $730
• D. $810

Correct answer: A

Rationale: The correct answer is $90. If he pays $270 per month in rent and saves a total of $360 per month, he puts $360 - $270 = $90 into his house savings account each month. Choice B ($270) is incorrect as this amount represents the rent paid, not the amount saved. Choices C ($730) and D ($810) are both significantly higher than the correct amount of $90, making them incorrect as they do not align with the given information in the question.

5. Jayden rides his bike for 5/8 miles. He takes a break and rides another 3/4 miles. How many miles does he ride?

• A. 1 3/8 miles
• B. 1 1/2 miles
• C. 1 7/8 miles
• D. 2 miles

Correct answer: A

Rationale: To find the total distance Jayden rides, you need to add the fractions 5/8 + 3/4. To add these fractions, you must ensure they have a common denominator. In this case, the common denominator is 8. So, 5/8 + 3/4 = 5/8 + 6/8 = 11/8. Since 11/8 can be simplified to 1 3/8, Jayden rides a total of 1 3/8 miles. Choice B (1 1/2 miles), Choice C (1 7/8 miles), and Choice D (2 miles) are incorrect as they do not accurately represent the total distance calculated by adding the two fractions, which is 1 3/8 miles.

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