Nursing Elites

1. Which of the following describes a proportional relationship?

• A. Johnathan opens a savings account with an initial deposit of $150 and deposits $125 per month
• B. Bruce pays his employees $12 per hour worked during the month of December, as well as a $250 bonus
• C. Alvin pays $28 per month for his phone service plus $0.07 for each long-distance minute used
• D. Kevin drives 65 miles per hour

Correct answer: A

Rationale: A proportional relationship is one in which two quantities vary directly with each other. In choice A, the amount deposited per month is directly proportional to the initial deposit. The relationship can be represented as y = 125x + 150, where x is the number of months and y is the total amount in the account. Choices B and C involve additional fixed amounts or variable costs that do not maintain a constant ratio, making them non-proportional relationships. Choice D refers to a constant speed of driving, which is not a proportional relationship as it does not involve varying quantities that change in direct proportion.

2. What is the result of adding 7/8 and 5/8 and expressing the sum in reduced form?

• A. 9/17
• B. 1/3
• C. 31/36
• D. 3/5

Correct answer: C

Rationale: To add 7/8 and 5/8, we combine the numerators while keeping the denominator the same: 7/8 + 5/8 = (7+5)/8 = 12/8. To simplify this fraction, we divide both the numerator and the denominator by their greatest common factor, which is 4. This yields 12/8 = 3/2. Therefore, the reduced form of 7/8 + 5/8 is 3/2, which is also equivalent to 1.5 as a mixed number. However, the question specifically asks for the answer in reduced form, making choice C, 3/2 or 31/36 after further simplification, the correct answer. Choices A, B, and D are incorrect because they do not represent the correct result of adding 7/8 and 5/8 in reduced form.

3. Solve for x: x + 5 = x - 3.

• A. x = -5
• B. x = 5
• C. x = -3
• D. x = 3

Correct answer: A

Rationale: To solve the equation x + 5 = x - 3, we aim to isolate x. By subtracting x from both sides, we get 5 = -3, which is not possible. This indicates that the equation has no solution. Therefore, the correct answer is x = -5. Choices B, C, and D are incorrect as they do not yield a valid solution when substituted back into the original equation.

4. A lab technician took 500 milliliters of blood from a patient. The technician used 1/6 of the blood for further tests. How many milliliters of blood were used for further tests? Round your answer to the nearest hundredth.

• A. 83
• B. 83.3
• C. 83.33
• D. 83.34

Correct answer: C

Rationale: To find 1/6 of 500, multiply 500 by 1/6: (500)(1/6) = 500/6 = 83.33. Converting the fraction to a decimal gives 83.33. Rounding this to the nearest hundredth results in 83.33. Therefore, 83.33 milliliters of blood were used for further tests. Choice A is incorrect as it does not consider the decimal value of the fraction. Choice B is incorrect as it rounds to the tenths place, not the nearest hundredth. Choice D is incorrect as it rounds up unnecessarily, as the correct answer should be rounded to 83.33.

5. A triangle has dimensions of 9 cm, 4 cm, and 7 cm. The triangle is reduced by a scale factor of x. Which of the following represents the dimensions of the dilated triangle?

• A. 8.25 cm, 3.25 cm, 6.25 cm
• B. 4.5 cm, 2 cm, 3.5 cm
• C. 6.75 cm, 3 cm, 5.25 cm
• D. 4.95 cm, 2.2 cm, 3.85 cm

Correct answer: C

Rationale: When reducing a figure by a scale factor, each dimension is multiplied by the same scale factor. In this case, the scale factor is not provided in the question. To find the scale factor, you would divide the new lengths of the sides by the original lengths. The scaled-down triangle's dimensions are the original dimensions multiplied by the scale factor. By performing the calculations, the dimensions of the dilated triangle are 6.75 cm, 3 cm, and 5.25 cm, which matches choice C. Choices A, B, and D have incorrect dimensions as they do not result from the correct application of the scale factor to the original triangle's dimensions.

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