Nursing Elites

1. A gumball machine contains red, orange, yellow, green, and blue gumballs. Twenty percent of the gumballs are red, 30% are orange, 5% are yellow, 10% are green, and the rest are blue. If there are a total of 120 gumballs, how many more blue gumballs are there than yellow gumballs?

• A. 48
• B. 30
• C. 42
• D. 36

Correct answer: D

Rationale: The percentage of blue gumballs is 35% (100% - 20% - 30% - 5% - 10% = 35%). If there are 120 gumballs, 35% of that is 42 blue gumballs. Since 5% are yellow gumballs, which is 6 gumballs, the difference between 42 blue gumballs and 6 yellow gumballs is 36 more blue gumballs. Therefore, the correct answer is 36. Choice A (48) is incorrect as it miscalculates the difference. Choice B (30) is incorrect as it does not consider the correct percentage of blue gumballs. Choice C (42) is incorrect as it miscalculates the difference between blue and yellow gumballs.

2. Complete the following equation: x + x * x - x / x = ?

• A. 5
• B. 3
• C. 2
• D. 1

Correct answer: B

Rationale: To solve the equation x + x * x - x / x, follow the order of operations (PEMDAS/BODMAS). First, perform the multiplication: x * x = x^2. Then, perform the division: x / x = 1. Substituting these back into the equation gives x + x^2 - 1. Therefore, the equation simplifies to x + x^2 - 1. By evaluating this further, the final result is 3. Choices A, C, and D are incorrect because they do not correctly apply the order of operations to solve the equation.

3. Dr. Lee observed that 30% of all his patients developed an infection after taking a certain antibiotic. He further noticed that 5% of those 30% required hospitalization to recover from the infection. What percentage of Dr. Lee's patients were hospitalized after taking the antibiotic?

• A. 1.50%
• B. 5%
• C. 15%
• D. 30%

Correct answer: C

Rationale: Out of all the patients who took the antibiotic, 30% developed an infection. Among those with infections, 5% required hospitalization. To find the percentage of all patients hospitalized, we multiply the two percentages: 30% * 5% = 1.5%. Therefore, 1.5% of all patients were hospitalized. Choice A (1.50%) is the calculated percentage of all patients hospitalized, not 1.50%. Choice B (5%) is the percentage of patients who developed an infection and required hospitalization, not all patients. Choice D (30%) represents the initial percentage of patients who developed an infection, not the percentage hospitalized.

4. Simplify the following expression: 5 x 3 ÷ 9 x 4

• A. 5/12
• B. 8/13
• C. 20/27
• D. 47/36

Correct answer: A

Rationale: To simplify the expression 5 x 3 ÷ 9 x 4, first perform the multiplications and divisions from left to right: 5 x 3 = 15 and 9 x 4 = 36. So, the expression becomes 15 ÷ 36. When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. Hence, 15 ÷ 36 = 15/36. To simplify the fraction further, find the greatest common divisor, which is 3. Divide both the numerator and denominator by 3 to get the final result: 15/36 = 5/12. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not represent the correct simplification of the given expression.

5. Simplify the expression. Which of the following is the value of x? (5(4x – 5) = (3/2)(2x – 6))

• A. −(2/7)
• B. −(4/17)
• C. (16/17)
• D. (8/7)

Correct answer: C

Rationale: To solve the given proportion 5(4x – 5) = (3/2)(2x – 6), first distribute to get 20x - 25 = 3x - 9. Then, simplify the linear equation by isolating x: 20x - 3x = 25 - 9, which leads to 17x = 16. Finally, solving for x gives x = 16/17. Choice A is incorrect as it does not match the calculated value of x. Choice B is incorrect as it does not correspond to the correct solution for x. Choice D is incorrect as it does not align with the accurate value of x obtained from solving the equation.

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