Which of the following inequalities is true?
- A. 0.7 < 0.1 < 0.11 < 0.101
- B. 0.1 < 0.7 < 0.101 < 0.11
- C. 0.1 < 0.7 < 0.11 < 0.101
- D. 0.1 < 0.101 < 0.11 < 0.7
Correct Answer & Rationale
Correct Answer: D
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
Other Related Questions
165 is what percent of 150?
- A. 95%
- B. 110%
- C. 111%
- D. 115%
Correct Answer & Rationale
Correct Answer: B
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.
Frederica used 13.4 gallons of gasoline to drive 448.9 miles. What was the average number of miles she drove per gallon of gasoline?
- A. 3.4 mpg
- B. 33.5 mpg
- C. 60.15 mpg
- D. 435.5 mpg
Correct Answer & Rationale
Correct Answer: B
To find the average miles per gallon (mpg), divide the total miles driven by the gallons used. Here, 448.9 miles divided by 13.4 gallons equals approximately 33.5 mpg. Option A (3.4 mpg) is incorrect as it significantly underestimates the fuel efficiency. Option C (60.15 mpg) overestimates the efficiency, suggesting an unrealistic performance for a typical vehicle. Option D (435.5 mpg) is also incorrect, as it implies an implausibly high efficiency that is not achievable with conventional vehicles. Thus, the calculation confirms that 33.5 mpg accurately represents Frederica's fuel efficiency.
To find the average miles per gallon (mpg), divide the total miles driven by the gallons used. Here, 448.9 miles divided by 13.4 gallons equals approximately 33.5 mpg. Option A (3.4 mpg) is incorrect as it significantly underestimates the fuel efficiency. Option C (60.15 mpg) overestimates the efficiency, suggesting an unrealistic performance for a typical vehicle. Option D (435.5 mpg) is also incorrect, as it implies an implausibly high efficiency that is not achievable with conventional vehicles. Thus, the calculation confirms that 33.5 mpg accurately represents Frederica's fuel efficiency.
John worked at a bookstore for two weeks. The second week he earned 20 percent more than he did the first week. If he earned $300 the second week, how much did he earn the first week?
- A. 240
- B. 250
- C. 280
- D. 380
Correct Answer & Rationale
Correct Answer: B
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.
60 ÷ 3/3 =
- A. 20
- B. 21
- C. 23
- D. 24
Correct Answer & Rationale
Correct Answer: A
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.