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
76 ÷ 0.01 =
- A. 0.76
- B. 7.6
- C. 760
- D. 7,600
Correct Answer & Rationale
Correct Answer: D
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.
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.
Fred worked 39.5 hours last week. Alice worked 6.75 fewer hours than Fred. How many hours did Alice work?
- A. 33.75 HOURS
- B. 33.25 HOURS
- C. 33.35 HOURS
- D. 33.85 HOURS
Correct Answer & Rationale
Correct Answer: A
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.
To determine the equivalence to 1.04, we can convert each fraction to a decimal. Option A, 52/51, equals approximately 1.0196, which is less than 1.04. Option B, 51/50, equals 1.02, also less than 1.04. Option C, 27/25, equals 1.08, exceeding 1.04. Option D, 26/25, simplifies to 1.04, matching the target value exactly. Thus, only option D accurately represents 1.04, while the others deviate from this value.