Nursing Elites

1. What is the probability of consecutively pulling two more orange blocks, without replacement, from a bag containing 3 orange blocks, 5 green blocks, and 4 purple blocks?

• A. 3/12
• B. 3/55
• C. 2/10
• D. 1/3

Correct answer: B

Rationale: To calculate the probability of consecutively pulling two more orange blocks without replacement, we first determine the probability of pulling an orange block on the first draw, which is 3/12 (3 orange blocks out of 12 total blocks). After removing one orange block, there are only 11 blocks left, so the probability of pulling another orange block on the second draw is 2/11. To find the combined probability, we multiply the probabilities together: (3/12) * (2/11) = 6/132 = 3/55. Therefore, the correct answer is B. Choice A (3/12) incorrectly simplifies the probability before calculating the second draw. Choice C (2/10) does not consider the specific number of orange blocks in the bag. Choice D (1/3) does not account for the reduced number of blocks after the first draw.

2. A closet is filled with red, blue, and green shirts. If 1/4 of the shirts are green and 1/3 are red, what fraction of the shirts are blue?

• A. 1/2
• B. 1/3
• C. 5/12
• D. 1/4

Correct answer: C

Rationale: Let the total number of shirts be x. Given that 1/4 of the shirts are green and 1/3 are red, we have Green = x/4 and Red = x/3. To find the fraction of blue shirts, we subtract the fractions of green and red shirts from 1: Blue fraction = 1 - (1/4 + 1/3) = 1 - (3/12 + 4/12) = 1 - 7/12 = 5/12. Therefore, the fraction of blue shirts is 5/12. Choices A, B, and D are incorrect because they do not accurately represent the fraction of blue shirts given the information provided.

3. 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.

4. What is the perimeter of a square with a side length of 6 cm?

• A. 24 cm
• B. 12 cm
• C. 18 cm
• D. 36 cm

Correct answer: A

Rationale: The perimeter of a square is calculated by multiplying the side length by 4 since all sides are equal. In this case, the side length is 6 cm, so the perimeter is 4 * 6 = 24 cm. Therefore, choice A, 24 cm, is the correct answer. Choices B, C, and D are incorrect because they do not reflect the correct calculation for the perimeter of a square.

5. Given the histograms shown below, which of the following statements is true?

• A. Group A is negatively skewed and has a mean less than Group B.
• B. Group A is positively skewed and has a mean greater than Group B.
• C. Group B is negatively skewed and has a mean greater than Group A.
• D. Group B is positively skewed and has a mean less than Group A.

Correct answer: C

Rationale: The correct answer is C. Group B is negatively skewed, indicating more high scores, leading to a higher mean for Group B when compared to Group A. Choice A is incorrect because Group A is not negatively skewed and doesn't have a mean less than Group B. Choice B is incorrect as Group A is not positively skewed and its mean is not greater than Group B. Choice D is also incorrect because Group B having a mean less than Group A contradicts the fact that Group B has a higher mean due to being negatively skewed.

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