Nursing Elites

1. University Q has an extremely competitive nursing program. Historically, 3/4 of the students in each incoming class major in nursing, but only 1/3 of those who major in nursing actually complete the program. If this year’s incoming class has 100 students, how many students will complete the nursing program?

• A. 75
• B. 20
• C. 25
• D. 5

Correct answer: C

Rationale: Out of 100 students, 3/4 major in nursing, which is 75 students (100 * 3/4 = 75). Among these 75 students, only 1/3 will complete the program. Therefore, 1/3 of 75 is 25. Hence, 25 students will complete the nursing program. Choice A (75) is incorrect because this represents the number of students majoring in nursing, not completing the program. Choices B (20) and D (5) are incorrect as they do not align with the calculation based on the given fractions and total number of students.

2. What is the simplest way to write the following expression? 5x - 2y + 4x + y

• A. 9x - y
• B. 9x - 3y
• C. 9x + 3y
• D. x; y

Correct answer: A

Rationale: To simplify the given expression 5x - 2y + 4x + y, we combine like terms. Grouping the x terms together and the y terms together, we have 5x + 4x - 2y + y. Combining like terms results in 9x - y. Therefore, the simplest form of the expression is 9x - y, which corresponds to option A. Option B is incorrect because it incorrectly subtracts 3y instead of just y. Option C is incorrect because it adds 3y instead of subtracting y. Option D is incorrect as it separates x and y with a semicolon instead of an operation, providing no simplified expression.

3. How much hydrochloric acid (HCl) is necessary to make 2.5 liters of a 5:1 solution of water (in liters) to HCl (in grams)?

• A. 0.5 grams
• B. 2 grams
• C. 5 grams
• D. 12.5 grams

Correct answer: C

Rationale: To create a 5:1 solution in 2.5 liters, 0.5 liters are needed for HCl, which translates to 5 grams. The correct answer is 5 grams, as this amount corresponds to the 5:1 ratio specified in the solution. Choices A, B, and D are incorrect because they do not align with the 5:1 ratio and the volume of the solution.

4. Which of the following is listed in order from least to greatest? (-2, -3/4, -0.45, 3%, 0.36)

• A. -2, -3/4, -0.45, 3%, 0.36
• B. -3/4, -0.45, -2, 0.36, 3%
• C. -0.45, -2, -3/4, 3%, 0.36
• D. -2, -3/4, -0.45, 0.36, 3%

Correct answer: A

Rationale: To determine the order from least to greatest, convert all the values to a common form. When written in decimal form, the order is -2, -0.75 (which is equal to -3/4), -0.45, 0.03 (which is equal to 3%), and 0.36. Therefore, the correct order is -2, -3/4, -0.45, 3%, 0.36 (Choice A). Choice B is incorrect as it has the incorrect placement of -2 and 0.36. Choice C is incorrect as it incorrectly places -0.45 before -2. Choice D is incorrect as it incorrectly places 0.36 before 3%.

5. As part of a study, a set of patients will be divided into three groups. 4/15 of the patients will be in Group Alpha, 2/5 in Group Beta, and 1/3 in Group Gamma. Order the groups from smallest to largest, according to the number of patients in each group.

• A. Group Alpha, Group Beta, Group Gamma
• B. Group Alpha, Group Gamma, Group Beta
• C. Group Gamma, Group Alpha, Group Beta
• D. Group Alpha, Group Beta, Group Gamma

Correct answer: B

Rationale: The correct order is Group Alpha, Group Gamma, Group Beta based on the common denominators of the fractions. To determine the order from smallest to largest, compare the fractions' numerators since the denominators are different. Group Alpha has 4/15 patients, Group Gamma has 1/3 patients, and Group Beta has 2/5 patients. Comparing the fractions' numerators, the order from smallest to largest is Group Alpha (4), Group Gamma (1), and Group Beta (2). Therefore, the correct order is Group Alpha, Group Gamma, Group Beta. Choice A is incorrect as it lists Group Beta before Group Gamma. Choice C is incorrect as it lists Group Gamma before Group Alpha. Choice D is incorrect as it lists Group Beta before Group Gamma, which is not in ascending order based on the number of patients.

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