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Ratio and proportion: 0.1:10::x:400
- A. 5
- B. 4
- C. 25
- D. 50
Correct Answer: B
Rationale: In a ratio, the two parts are related by a proportion. To find the missing value, x, in the given ratio, you need to set up a proportion. Given: 0.1:10::x:400. Cross multiply to solve for x: 0.1 * 400 = 10 * x, which simplifies to x = (0.1 * 400) / 10 = 4. Therefore, the correct answer is 4.
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How many meters are in 2 kilometers?
- A. 2000 meters
- B. 0.002 meters
- C. 20 meters
- D. 0.2 meters
Correct Answer: A
Rationale: To convert kilometers to meters, you need to multiply by 1000 because there are 1000 meters in 1 kilometer. Therefore, 2 kilometers is equal to 2 x 1000 = 2000 meters. The correct answer is 2000 meters. This conversion is a fundamental mathematical operation used across different fields, such as science, engineering, and day-to-day measurements, to accurately convert between larger and smaller units of length.
How many ounces are in 3 5/8 quarts?
- A. 32
- B. 116
- C. 96
- D. 928/8
Correct Answer: B
Rationale: To convert quarts to ounces, we use the conversion factor that 1 quart is equal to 32 ounces. To find how many ounces are in 3 5/8 quarts, first, we calculate the ounces in 3 quarts by multiplying 3 quarts by 32 ounces/quart, which equals 96 ounces. Then, we find the equivalent of 5/8 quart, which is 5/8 * 32 = 20 ounces. Adding the ounces from 3 quarts and 5/8 quart together, we get a total of 116 ounces. Therefore, the correct answer is 116 ounces.
Change 1/10 to a decimal.
- A. 0.001
- B. 0.1
- C. 0.01
- D. 0.0001
Correct Answer: B
Rationale: To change 1/10 to a decimal, divide the numerator (1) by the denominator (10). So, 1 ÷ 10 = 0.1. The correct answer is B (0.1). A (0.001), C (0.01), and D (0.0001) are incorrect as they do not represent the decimal equivalent of 1/10. A is 100 times smaller, C is 10 times smaller, and D is 1,000 times smaller than the correct answer.
A traveler left his house on Tuesday at 10:00 AM and arrived at his destination on Wednesday at 6:00 PM. He stopped twice for 30 minutes each time to get gas and food. He also stopped for a 4-hour nap on Wednesday. How long did he drive for?
- A. 28 hours
- B. 32 hours
- C. 27 hours
- D. 15 hours
Correct Answer: C
Rationale: To calculate the total driving time, first determine the time from Tuesday 10:00 AM to Wednesday 6:00 PM, which is 32 hours. Subtract the time spent on stops and nap, which is 30 minutes x 2 stops + 4 hours = 5 hours. Therefore, the driving time is 32 hours - 5 hours = 27 hours. This means the traveler drove for 27 hours, making choice C the correct answer.
Ratio and Proportion: 450:15::225:X
- A. X=15
- B. X=75
- C. X=30
- D. X=60
Correct Answer: C
Rationale: To find X in the proportion 450:15::225:X, we need to set up a ratio equation. The ratio 450:15 simplifies to 30:1 (by dividing both sides by 15). So, the proportion becomes 30:1::225:X. To find X, we cross multiply: 30 * X = 225 * 1. Solving for X, we get X = 225/30 = 7.5. Therefore, the correct answer is C: X=30.
Rationale:
A) X=15 is incorrect because it does not follow the ratio relationship.
B) X=75 is incorrect as it is not the result of the ratio calculation.
D) X=60 is incorrect because it does not align with the correct ratio computation.