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
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.
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.
2 + (2 × 2) + 2 =
- A. 8
- B. 10
- C. 12
- D. 16
Correct Answer & Rationale
Correct Answer: A
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
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.