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A person drives 300 miles at 60 mph, then another 200 miles at 80 mph, with a 30-minute break. How long does the trip take?
- A. 5.5 hours
- B. 7 hours
- C. 6 hours
- D. 4.5 hours
Correct Answer: C
Rationale: To find the total time, we calculate the time taken for each segment: 300 miles at 60 mph = 300 miles · 60 mph = 5 hours; 200 miles at 80 mph = 200 miles · 80 mph = 2.5 hours. Adding these gives 5 hours + 2.5 hours = 7.5 hours. Converting the 30-minute break to hours (30 minutes · 60 = 0.5 hours), the total time taken is 7.5 hours + 0.5 hours = 8 hours. Therefore, the correct answer is not among the given choices. The rationale provided in the original question is incorrect as it does not account for the break time and has a calculation error in adding the individual times.
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A student scores 85% on a test with 50 questions. How many questions did the student answer correctly?
- A. 40 questions
- B. 42 questions
- C. 43 questions
- D. 45 questions
Correct Answer: C
Rationale: To find the number of questions answered correctly, you multiply the percentage (85%) by the total number of questions (50). 85% of 50 questions is 0.85 * 50 = 43 questions answered correctly. Therefore, the correct answer is 43 questions. Choices A, B, and D are incorrect as they do not reflect the accurate calculation based on the given information.
A car travels 60 miles in 1 hour. How long will it take to travel 180 miles at the same speed?
- A. 3 hours
- B. 4 hours
- C. 2.5 hours
- D. 5 hours
Correct Answer: A
Rationale: To find the time needed to travel 180 miles at the same speed of 60 miles per hour, you divide the total distance by the speed. 180 miles · 60 mph = 3 hours. Therefore, it will take 3 hours to travel 180 miles at the given speed. Choice B, 4 hours, is incorrect as it does not align with the calculation. Choice C, 2.5 hours, is incorrect as it underestimates the time needed for the distance. Choice D, 5 hours, is incorrect as it overestimates the time required based on the given speed.
University Q has an extremely competitive nursing program. Historically, 3/4 of the students in each incoming class major in nursing, but only 1/3 of those who major in nursing actually complete the program. If this year's incoming class has 100 students, how many students will complete the nursing program?
- A. 75
- B. 20
- C. 25
- D. 5
Correct Answer: C
Rationale: Out of 100 students, 3/4 major in nursing, which is 75 students (100 * 3/4 = 75). Among these 75 students, only 1/3 will complete the program. Therefore, 1/3 of 75 is 25. Hence, 25 students will complete the nursing program. Choice A (75) is incorrect because this represents the number of students majoring in nursing, not completing the program. Choices B (20) and D (5) are incorrect as they do not align with the calculation based on the given fractions and total number of students.
Veronica is making a holiday schedule. 35% of staff members will be on vacation, and 20% of the remainder are certified to work. What percentage of the staff is certified and available?
- A. 0.07
- B. 0.13
- C. 0.65
- D. 0.8
Correct Answer: A
Rationale: To find the percentage of staff certified and available, we first calculate the percentage of staff members not on vacation, which is 100% - 35% = 65%. Then, 20% of this group is certified to work, which is 20% of 65% = 0.20 * 65% = 13%. Therefore, Veronica has 13% of the staff certified and available to work. The correct answer is 0.13 (or 13%).
Choice C (0.65) is incorrect because it represents the percentage of staff members not on vacation, not the percentage that is certified and available. Choice D (0.8) is incorrect as it is not the correct percentage of staff members certified and available. Choice B (0.13) is the correct answer, not choice A (0.07), as 0.07 represents 7%, not 13%.
As part of a study, a set of patients will be divided into three groups: 1/2 of the patients will be in Group Alpha, 1/3 of the patients will be in Group Beta, and 1/6 of the patients will be in Group Gamma. Order the groups from smallest to largest, according to the number of patients in each group.
- A. Group Alpha, Group Beta, Group Gamma
- B. Group Alpha, Group Gamma, Group Beta
- C. Group Gamma, Group Alpha, Group Beta
- D. Group Gamma, Group Beta, Group Alpha
Correct Answer: C
Rationale: The correct order from smallest to largest number of patients in each group is Group Gamma (1/6), Group Alpha (1/2), and Group Beta (1/3). Group Gamma has the smallest fraction of patients, followed by Group Alpha and then Group Beta. Therefore, choice C, 'Group Gamma, Group Alpha, Group Beta,' is the correct answer. Choices A, B, and D are incorrect because they do not follow the correct order based on the fractions of patients assigned to each group.