Nursing Elites

1. What is the least common denominator of two fractions?

• A. The smallest number that is a multiple of both denominators
• B. The smallest number that both fractions can divide into evenly
• C. The least common multiple of both denominators
• D. The greatest common factor of both denominators

Correct answer: C

Rationale: The least common denominator of two fractions is the least common multiple of both denominators. This is because the least common denominator is the smallest number that both denominators can divide into evenly, ensuring that both fractions can be expressed with a common denominator. Choice A is incorrect as the least common denominator is a multiple of both denominators, not a number that multiplies into both. Choice B is incorrect because the common denominator needs to be a multiple of both denominators, not just a number they can divide into evenly. Choice D is incorrect as the greatest common factor is not used to find the least common denominator, but rather the least common multiple.

2. In a study on anorexia, 100 patients participated. Among them, 70% were women, and 10% of the men were overweight as children. How many male patients in the study were not overweight as children?

• A. 3
• B. 10
• C. 27
• D. 30

Correct answer: C

Rationale: Out of the 100 patients, 30% were men. Since 10% of the men were overweight as children, 90% of the male patients were not overweight. Therefore, the number of male patients not overweight as children can be calculated as 30 (total male patients) x 0.90 = 27. Choices A, B, and D are incorrect because they do not accurately calculate the number of male patients who were not overweight as children based on the given information.

3. Solve for x: 3(x - 5) = 2(x + 3)

• A. x = 3
• B. x = 6
• C. x = 9
• D. x = 12

Correct answer: A

Rationale: To solve the equation 3(x - 5) = 2(x + 3) for x, start by distributing the terms inside the parentheses. This gives you 3x - 15 = 2x + 6. Next, combine like terms by moving all terms with x to one side and the constants to the other side. Subtracting 2x from both sides gives x - 15 = 6. Finally, adding 15 to both sides results in x = 21. Therefore, the correct answer is A: x = 3. Choices B, C, and D are incorrect as they do not result from the correct calculations of the equation.

4. A book has a width of 2.5 decimeters. What is the width of the book in centimeters?

• A. 0.25 centimeters
• B. 25 centimeters
• C. 250 centimeters
• D. 0.025 centimeters

Correct answer: B

Rationale: To convert decimeters to centimeters, we use the conversion factor that 1 decimeter is equal to 10 centimeters. Setting up the proportion: 1/0.1 = x/2.5. Solving for x gives 2.5 = 0.1x, x = 25. Therefore, the width of the book in centimeters is 25. Choices A, C, and D are incorrect because they do not correctly convert decimeters to centimeters. A and D have decimal placement errors, and C has an incorrect magnitude of centimeters.

5. 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.

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