19. The list shown gives the number of movies that each of six of Sam's friends saw last year: 12, 17, 9, 11, 12, 14. Sam's sister Lucy saw 7 fewer movies last year than Sam did. The range of the numbers of movies that Sam, Lucy, and each of the six friends saw last year was 10. Which of the following could be the number of movies that Sam saw last year?
Answer: A
Sam could have seen 14 movies last year.
Given that the range of the numbers of movies seen by Sam, Lucy, and Sam's six friends is 10, we can deduce that if Sam saw 14 movies, then Lucy would have seen 7 fewer, making it 7 movies. This fits within the range established by Sam's friends, which is 9 (the lowest) to 17 (the highest).
A) 14
This option is correct because if Sam saw 14 movies, Lucy would have seen 7. The highest number of movies seen by Sam's friends is 17, and the lowest is 9. The range (17 - 7 = 10) fits perfectly, confirming that the range is indeed 10.
B) 15
If Sam saw 15 movies, Lucy would have seen 8. The range would then be from 8 to 17, which would yield a range of 9 (17 - 8 = 9). This does not satisfy the condition of a range of 10, making this option incorrect.
C) 16
Should Sam have seen 16 movies, Lucy would have seen 9. This would give a range from 9 to 17 (17 - 9 = 8), which again fails to meet the requirement of a range of 10, thus making this option incorrect.
D) 17
If Sam saw 17 movies, then Lucy would have seen 10. This would give a range from 10 to 17 (17 - 10 = 7), which is not equal to 10, meaning this option is incorrect.
E) 18
If Sam saw 18 movies, Lucy would have seen 11. The range from 11 to 18 (18 - 11 = 7) does not satisfy the requirement of a range of 10, rendering this option incorrect as well.
Conclusion
The only option that meets the requirement of maintaining a range of 10 is 14, as it allows for Lucy's count to be 7, effectively fitting within Sam's friends' counts. All other options fail to establish the necessary range, confirming that 14 is the only viable answer.