A company employee generates a series of five-digit product codes in accordance with the following rules: The codes use the digits 0, 1, 2, 3, and 4, and no others. Each digit occurs exactly once in any code. The second digit has a value exactly twice that of the first digit. The value of the third digit is less than the value of the fifth digit. Questions 1–5 1. If the last digit of an acceptable product code is 1, it must be true that the

2. Which one of the following must be true about any acceptable product code?

3. If the third digit of an acceptable product code is not 0, which one of the following must be true?

4. Any of the following pairs could be the third and fourth digits, respectively, of an acceptable product code, EXCEPT:

5. Which one of the following must be true about any acceptable product code?

Exactly three films—Greed, Harvest, and Limelight—are shown during a film club’s festival held on Thursday, Friday, and Saturday. Each film is shown at least once during the festival but never more than once on a given day. On each day at least one film is shown. Films are shown one at a time. The following conditions apply: On Thursday Harvest is shown, and no film is shown after it on that day. On Friday either Greed or Limelight, but not both, is shown, and no film is shown after it on that day. On Saturday either Greed or Harvest, but not both, is shown, and no film is shown after it on that day. 6. Which one of the following could be a complete and accurate description of the order in which the films are shown at the festival?

7. Which one of the following CANNOT be true?

8. If Limelight is never shown again during the festival once Greed is shown, then which one of the following is the maximum number of film showings that could occur during the festival?

9. If Greed is shown exactly three times, Harvest is shown exactly twice, and Limelight is shown exactly once, then which one of the following must be true?

10. If Limelight is shown exactly three times, Harvest is shown exactly twice, and Greed is shown exactly once, then which one of the following is a complete and accurate list of the films that could be the first film shown on Thursday?