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.
Other Related Questions
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.
A book is on sale for 25% off. If the original price of the book was D dollars, what is the sale price, in dollars, in terms of D?
- A. D - 25
- B. 7.5D
- C. 0.75D
- D. 0.25D
Correct Answer & Rationale
Correct Answer: C
To find the sale price of a book that is 25% off, we first calculate the discount amount, which is 25% of the original price D. This can be expressed as 0.25D. The sale price is then the original price minus the discount, or D - 0.25D, which simplifies to 0.75D. Option A (D - 25) incorrectly subtracts a fixed dollar amount rather than a percentage, making it irrelevant to the problem. Option B (7.5D) mistakenly applies the percentage in a way that inflates the price instead of reducing it. Option D (0.25D) represents only the discount amount, not the sale price. Thus, 0.75D accurately reflects the sale price after applying the discount.
To find the sale price of a book that is 25% off, we first calculate the discount amount, which is 25% of the original price D. This can be expressed as 0.25D. The sale price is then the original price minus the discount, or D - 0.25D, which simplifies to 0.75D. Option A (D - 25) incorrectly subtracts a fixed dollar amount rather than a percentage, making it irrelevant to the problem. Option B (7.5D) mistakenly applies the percentage in a way that inflates the price instead of reducing it. Option D (0.25D) represents only the discount amount, not the sale price. Thus, 0.75D accurately reflects the sale price after applying the discount.
1 is 3 percent of what number?
- A. 1/3
- B. 3
- C. 30
- D. 33,1/3
Correct Answer & Rationale
Correct Answer: D
To find the number of which 1 is 3 percent, set up the equation: 1 = 0.03 × x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a fraction far smaller than 1. Option B (3) fails because 3 percent of 3 is 0.09, not 1. Option C (30) is also incorrect; 3 percent of 30 equals 0.9. Thus, only option D (33 1/3) correctly satisfies the equation, making it the right choice.
To find the number of which 1 is 3 percent, set up the equation: 1 = 0.03 × x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a fraction far smaller than 1. Option B (3) fails because 3 percent of 3 is 0.09, not 1. Option C (30) is also incorrect; 3 percent of 30 equals 0.9. Thus, only option D (33 1/3) correctly satisfies the equation, making it the right choice.
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.