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
If a number rounded to the nearest hundredth is 9.99, which of the following could be the number?
- A. 9.845
- B. 9.983
- C. 9.992
- D. 9.998
Correct Answer & Rationale
Correct Answer: C
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.
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.
The coordinate of pointP on the number line above is x. The value of 10x is between
- A. 1 and 4
- B. 4 and 6
- C. 6 and 8
- D. 8 and 12
Correct Answer & Rationale
Correct Answer: B
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
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.