For all positive integers n, let n be defined as the sum of the positive divisors of n. For example, bullet 9 = 1 + 3 + 9 = 13. Which of the following is equal to 16 - 15?
- A. 41
- B. 3
- C. 4
- D. 5
Correct Answer & Rationale
Correct Answer: C
To solve the expression 16 - 15, we first perform the subtraction, which yields 1. Now, examining the options: A: 41 is incorrect as it does not equal 1. B: 3 is also incorrect, as it is greater than 1. C: 4 is the only option that meets the criteria, but it is not equal to 1, making it incorrect as well. D: 5 is incorrect for the same reason; it does not equal 1. None of the options accurately represent the result of 16 - 15, which is 1. The question seems to have an error in its provided options, as none align with the correct calculation.
To solve the expression 16 - 15, we first perform the subtraction, which yields 1. Now, examining the options: A: 41 is incorrect as it does not equal 1. B: 3 is also incorrect, as it is greater than 1. C: 4 is the only option that meets the criteria, but it is not equal to 1, making it incorrect as well. D: 5 is incorrect for the same reason; it does not equal 1. None of the options accurately represent the result of 16 - 15, which is 1. The question seems to have an error in its provided options, as none align with the correct calculation.
Other Related Questions
Point C is the center of the regular hexagon shown above. Which of the following expressions represents the area of this hexagon?
- A. 12xy
- B. 6xy
- C. 3xy
- D. xy
Correct Answer & Rationale
Correct Answer: B
The area of a regular hexagon can be calculated using the formula \( \frac{3\sqrt{3}}{2} s^2 \), where \( s \) is the length of a side. The expression \( 6xy \) aligns with this area formula when considering specific dimensions of the hexagon defined by \( x \) and \( y \). Option A, \( 12xy \), overestimates the area, suggesting a larger hexagon than the dimensions allow. Option C, \( 3xy \), and Option D, \( xy \), both underestimate the area, not accounting for the full extent of the hexagon's geometry. Thus, \( 6xy \) accurately represents the area based on the given variables.
The area of a regular hexagon can be calculated using the formula \( \frac{3\sqrt{3}}{2} s^2 \), where \( s \) is the length of a side. The expression \( 6xy \) aligns with this area formula when considering specific dimensions of the hexagon defined by \( x \) and \( y \). Option A, \( 12xy \), overestimates the area, suggesting a larger hexagon than the dimensions allow. Option C, \( 3xy \), and Option D, \( xy \), both underestimate the area, not accounting for the full extent of the hexagon's geometry. Thus, \( 6xy \) accurately represents the area based on the given variables.
3√2- 2/(√2) =
- A. 2√2
- B. √2
- C. 3
- D. 4
Correct Answer & Rationale
Correct Answer: A
To solve the expression \( 3\sqrt{2} - \frac{2}{\sqrt{2}} \), we first simplify \( \frac{2}{\sqrt{2}} \). This can be rewritten as \( \frac{2\sqrt{2}}{2} = \sqrt{2} \). Thus, the expression becomes \( 3\sqrt{2} - \sqrt{2} \), which simplifies to \( 2\sqrt{2} \). Option B (\( \sqrt{2} \)) is incorrect as it does not account for the subtraction from \( 3\sqrt{2} \). Option C (3) is incorrect because it misrepresents the value obtained after simplification. Option D (4) is also incorrect, as it does not relate to the expression at all.
To solve the expression \( 3\sqrt{2} - \frac{2}{\sqrt{2}} \), we first simplify \( \frac{2}{\sqrt{2}} \). This can be rewritten as \( \frac{2\sqrt{2}}{2} = \sqrt{2} \). Thus, the expression becomes \( 3\sqrt{2} - \sqrt{2} \), which simplifies to \( 2\sqrt{2} \). Option B (\( \sqrt{2} \)) is incorrect as it does not account for the subtraction from \( 3\sqrt{2} \). Option C (3) is incorrect because it misrepresents the value obtained after simplification. Option D (4) is also incorrect, as it does not relate to the expression at all.
Trevani bought a book. She paid a total of $13.50, including 8% sales tax. How much tax did Trevani pay on the book?
- A. $0.96
- B. $1.00
- C. $1.04
- D. $1.08
Correct Answer & Rationale
Correct Answer: B
To find the amount of sales tax Trevani paid, first determine the price before tax. The total amount paid, $13.50, includes an 8% tax. To find the pre-tax amount, divide the total by 1.08 (which accounts for the original price plus tax): $13.50 ÷ 1.08 = $12.50. Next, calculate the sales tax by subtracting the pre-tax amount from the total: $13.50 - $12.50 = $1.00. This confirms that Trevani paid $1.00 in tax. - Option A ($0.96) is incorrect as it underestimates the tax. - Option C ($1.04) slightly overestimates the tax. - Option D ($1.08) incorrectly assumes the total is all tax without accounting for the book's price.
To find the amount of sales tax Trevani paid, first determine the price before tax. The total amount paid, $13.50, includes an 8% tax. To find the pre-tax amount, divide the total by 1.08 (which accounts for the original price plus tax): $13.50 ÷ 1.08 = $12.50. Next, calculate the sales tax by subtracting the pre-tax amount from the total: $13.50 - $12.50 = $1.00. This confirms that Trevani paid $1.00 in tax. - Option A ($0.96) is incorrect as it underestimates the tax. - Option C ($1.04) slightly overestimates the tax. - Option D ($1.08) incorrectly assumes the total is all tax without accounting for the book's price.
Lanelle traveled 9.7 miles of her delivery route in 1.2 hours. At this same rate, which of the following is closest to the time it will take for Janelle to travel 20 miles?
- A. 2 hours
- B. 2.5 hours
- C. 5 hours
- D. 5.5 hours
Correct Answer & Rationale
Correct Answer: B
To determine the time it will take for Janelle to travel 20 miles, we first calculate Lanelle's speed. She traveled 9.7 miles in 1.2 hours, giving a speed of approximately 8.08 miles per hour (9.7 miles ÷ 1.2 hours). Using this speed, we can find the time for 20 miles by dividing the distance by the speed: 20 miles ÷ 8.08 mph ≈ 2.48 hours, which rounds to about 2.5 hours. Option A (2 hours) underestimates the time based on Lanelle's speed. Options C (5 hours) and D (5.5 hours) greatly overestimate the time needed. Thus, 2.5 hours is the most accurate estimate for Janelle's travel time.
To determine the time it will take for Janelle to travel 20 miles, we first calculate Lanelle's speed. She traveled 9.7 miles in 1.2 hours, giving a speed of approximately 8.08 miles per hour (9.7 miles ÷ 1.2 hours). Using this speed, we can find the time for 20 miles by dividing the distance by the speed: 20 miles ÷ 8.08 mph ≈ 2.48 hours, which rounds to about 2.5 hours. Option A (2 hours) underestimates the time based on Lanelle's speed. Options C (5 hours) and D (5.5 hours) greatly overestimate the time needed. Thus, 2.5 hours is the most accurate estimate for Janelle's travel time.