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On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30 cm². What is the actual area of the room?
- A. 30,000 cm²
- B. 300 m²
- C. 3,000 m²
- D. 30 m²
Correct Answer: D
Rationale: On a 1:100 scale drawing, each centimeter represents one meter. The area of the room in the scale drawing is 30 cm², which means the actual area is 30 m². Choice A (30,000 cm²) is incorrect as it doesn't account for the scale conversion. Choice B (300 m²) is incorrect because it multiplies the scale area directly by 10,000, which is not the correct conversion. Choice C (3,000 m²) is also incorrect as it applies the scale factor incorrectly.
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How many milligrams are in 5 grams?
- A. 0.005 mg
- B. 50 mg
- C. 500 mg
- D. 5000 mg
Correct Answer: D
Rationale: To convert grams to milligrams, you need to multiply by 1000 since 1 gram is equal to 1000 milligrams. Therefore, 5 grams is equal to 5 * 1000 = 5000 milligrams. Choices A, B, and C are incorrect because they do not correctly convert grams to milligrams. Choice A is incorrect as it represents a decrease in value instead of an increase when converting from grams to milligrams. Choice B is incorrect because it is a factor of 10 lower than the correct answer. Choice C is incorrect as it is a factor of 10 lower than the correct answer. Thus, the correct answer is D, 5000 mg.
Simplify the following expression: (2/7) · (5/6)
- A. 2/5
- B. 35/15
- C. 5/21
- D. 12/35
Correct Answer: D
Rationale: To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. In this case, (2/7) · (5/6) becomes (2/7) (6/5) = 12/35. Therefore, the correct answer is 12/35. Choice A (2/5), choice B (35/15), and choice C (5/21) are incorrect because they do not correctly simplify the given expression.
The table below shows the number of books checked out from a library over the course of 4 weeks. Which equation describes the relationship between the number of books (b) and weeks (w)?
- A. b = 10w + 2
- B. b = 5w + 10
- C. b = 8w + 12
- D. b = 4w + 20
Correct Answer: B
Rationale: The relationship between the number of books and weeks is best described by the equation b = 5w + 10. This is because the initial value of books checked out is 10, which indicates that even with 0 weeks, there are already 10 books checked out. The rate at which books are checked out per week is 5, as indicated by the coefficient of w. Therefore, the correct equation should be b = 5w + 10. Choices A, C, and D are incorrect because they do not represent the correct initial value or rate of increase for the given scenario.
Robert scores three new clients every eight months. After how many months has he secured 24 new clients?
- A. 64
- B. 58
- C. 52
- D. 66
Correct Answer: A
Rationale: To find out the number of months needed to secure 24 new clients, you can set up a proportion: 3 clients / 8 months = 24 clients / x months. Cross multiplying gives you 3x = 24 * 8. Solving for x: 3x = 192, x = 192 / 3, x = 64. Therefore, Robert will secure 24 new clients after 64 months. Choice A is correct. Choice B (58), Choice C (52), and Choice D (66) are incorrect as they do not align with the correct calculation based on the given proportion.
What is the median of Pernell's scores (81, 92, 87, 89, and 94)?
- A. 87
- B. 89
- C. 92
- D. 94
Correct Answer: B
Rationale: To find the median, we first need to arrange the scores in ascending order: 81, 87, 89, 92, 94. Since there are five scores, the middle score would be the third one, which is 89. Hence, the median of Pernell's scores is 89. Choice A (87) is incorrect because it is the second score in the ordered list, not the middle one. Choice C (92) and Choice D (94) are also incorrect as they are not positioned in the middle of the ordered series.