SAT Math Multiple Choice Question 444: Answer and Explanation

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Question: 444

9. A college professor with several hundred students has office hours between classes to provide extra help when needed. His classes on Monday are from 9:00 AM to 10:45 AM and 2:30 PM to 3:45 PM. It takes him 5 minutes to walk from the classroom to his office, and he takes a lunch break from 12:00 PM to 1:00 PM. On a particular Monday, he plans to grade tests, which have all multiple-choice questions. If each test consists of 50 questions and it takes him 4 seconds to mark each question right or wrong, how many complete tests can he mark during his office hours if no students come for help? Assume that he does not take the time to add up the scores until after his afternoon class.

  • A. 46
  • B. 47
  • C. 54
  • D. 55

Correct Answer: A



Difficulty: Hard

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Strategic Advice: This question has a lot of information, so break the question into short steps. First, calculate the amount of time the professor will spend in office hours. Then, determine how many questions he can grade in that time, paying careful attention to units as you go.

Getting to the Answer: Start by finding the time between classes. There are 3 hours and 45 minutes between classes. Now, subtract 10 minutes (5 minutes each way) for walking to and from the classroom, which leaves 3 hours and 35 minutes. Next, subtract the hour the professor takes for lunch, leaving 2 hours and 35 minutes, to grade papers. Now comes the tricky part. The question gives you the rate at which he can grade papers per second, so you need to convert the hours and minutes to seconds. There are 60 minutes in 1 hour, so 2 hours and 35 minutes is 155 minutes. There are 60 seconds in 1 minute, so the number of seconds the professor has to grade papers is 9,300. Now divide this by 4 to see how many questions he can grade: 2,325. The question asks how many complete tests he can grade, and there are 50 questions per test, so divide by 50 to get 46.5, which means he can completely grade 46 tests (he doesn't have time to finish the 47th test).

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