Of the following, which is closest to 17/6 + 6/17 ?
- A. 1
- B. 2
- C. 3
- D. 23
Correct Answer & Rationale
Correct Answer: C
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.
To solve 17/6 + 6/17, we first find a common denominator, which is 102. Rewriting the fractions gives us (17*17)/(6*17) + (6*6)/(17*6) = 289/102 + 36/102 = 325/102. Dividing 325 by 102 yields approximately 3.19, which is closest to 3. Option A (1) is too low, as it does not account for the combined value of the fractions. Option B (2) is still below the calculated sum. Option D (23) is excessively high and not feasible given the values involved. Thus, option C (3) is the most accurate approximation.
Other Related Questions
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.
Marisol has 5 times as many books as Jerry. Jerry has 15 books. How many books does Marisol have?
- A. 10
- B. 20
- C. 75
- D. 225
Correct Answer & Rationale
Correct Answer: C
To determine how many books Marisol has, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.
To determine how many books Marisol has, start by recognizing that she has 5 times the number of books Jerry has. Since Jerry has 15 books, you multiply 15 by 5: 15 × 5 = 75. Thus, Marisol has 75 books. Option A (10) is incorrect as it suggests Marisol has fewer books than Jerry. Option B (20) also underestimates her total, as it does not account for the multiplication factor of 5. Option D (225) overestimates the total by incorrectly multiplying the number of Jerry's books. Only option C accurately reflects the calculation based on the relationship between Marisol's and Jerry's books.
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 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.