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In a 4-hour exam with 420 questions and 60 mathematics problems, how many minutes should be allocated for the mathematics problems if they require twice the time of other questions?

  1. 60 minutes

  2. 65 minutes

  3. 70 minutes

  4. 75 minutes

The correct answer is: 60 minutes

To determine how many minutes should be allocated for the mathematics problems, we start by establishing the total duration of the exam, which is 4 hours. This is equivalent to 240 minutes. Next, we have 420 questions in total, of which 60 are mathematics problems. The remaining 360 questions are of a different type. Since the mathematics questions require twice the time of the other questions, let's define the time required for one non-mathematics question as "x" minutes. Thus, the time required for one mathematics problem will be "2x" minutes. We can calculate the total time spent on the non-mathematics problems as follows: - Time for non-mathematics questions = 360 questions * x minutes = 360x minutes. - Time for mathematics questions = 60 questions * 2x minutes = 120x minutes. Adding these amounts gives the total time allocated for all questions: 360x + 120x = 480x minutes. Since the total available time for the exam is 240 minutes, we can set up the equation: 480x = 240. Solving for "x" gives: x = 240 / 480 = 0.5 minutes.