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.
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.
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.
3,1/2 × 2,1/3 =
- A. 8,1/6
- B. 7,5/6
- C. 6,1/6
- D. 5,5/6
Correct Answer & Rationale
Correct Answer: A
To solve 3 1/2 × 2 1/3, first convert the mixed numbers to improper fractions: 3 1/2 becomes 7/2 and 2 1/3 becomes 7/3. Multiplying these gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
To solve 3 1/2 × 2 1/3, first convert the mixed numbers to improper fractions: 3 1/2 becomes 7/2 and 2 1/3 becomes 7/3. Multiplying these gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
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.