Which of the following is equivalent to 8,1/4?
- A. 0.0825
- B. 0.825
- C. 8.25
- D. 82.5
Correct Answer & Rationale
Correct Answer: c
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
Other Related Questions
The chart above shows the store's cost and list price for three models of stoves sold by an appliance store.
During a 20 percent off sale, Gene bought a Model Y stove from this store. How much profit did the store
make on Gene's purchase? (Profit = Price paid - Store's cost)
- A. $260
- B. $380
- C. $590
- D. $760
Correct Answer & Rationale
Correct Answer: D
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.
To determine the profit made by the store on Gene's purchase of Model Y, first calculate the sale price. If the list price is $950, a 20% discount reduces it by $190, resulting in a sale price of $760. Next, subtract the store's cost of $0 from the sale price, yielding a profit of $760. Option A ($260) incorrectly assumes a lower sale price or higher cost. Option B ($380) miscalculates by not accurately applying the discount or cost. Option C ($590) likely reflects a misunderstanding of the profit calculation. Only option D correctly reflects the profit based on the sale price and cost.
Which of the labeled points on the number line above has coordinate closest to
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: D
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
Point D is closest to zero on the number line, making its coordinate the nearest to the origin. Points A, B, and C are further away from zero, with A being negative and C being a larger positive number. Point B, while positive, is also farther from zero than D. Thus, D represents the coordinate that is numerically closest to zero, confirming its position as the nearest point on the number line. Understanding the proximity of these points to zero is essential for accurately determining their coordinates.
If 32% of n is 20.8, what is n?
- A. 64
- B. 65
- C. 66
- D. 154
Correct Answer & Rationale
Correct Answer: B
To find \( n \), we start with the equation \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
To find \( n \), we start with the equation \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
If 4 is x percent of 16, what is x?
- A. 1/4
- B. 4
- C. 16
- D. 25
Correct Answer & Rationale
Correct Answer: D
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.