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?

Rationale

Sam could have seen 14 movies last year.

Given that the range of the number of movies seen by Sam, Lucy, and his six friends is 10, the maximum and minimum values in the combined dataset must be 10 units apart. If Sam saw 14 movies, Lucy would have seen 7 fewer, totaling 7 movies, which fits within the range established by the friends' counts.

A (14) CORRECT

If Sam saw 14 movies, then Lucy would have seen 7 movies (14 - 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 this scenario maintains the required range of 10.

B (15) YOUR ANSWER

If Sam saw 15 movies, Lucy would have seen 8 movies (15 - 7). The highest number of movies seen by friends is still 17. The range would then be 17 - 8 = 9, which does not satisfy the condition of a range of 10.

C (16) YOUR ANSWER

If Sam saw 16 movies, Lucy would have seen 9 movies (16 - 7). The range would be 17 - 9 = 8, again failing to meet the required range of 10.

D (17) YOUR ANSWER

If Sam saw 17 movies, Lucy would have seen 10 movies (17 - 7). The range would be 17 - 10 = 7, which does not meet the requirement of a range of 10 either.

E (18) YOUR ANSWER

If Sam saw 18 movies, Lucy would have seen 11 movies (18 - 7). The range would be 17 - 11 = 6, which is also insufficient to fulfill the 10-unit range requirement.

Conclusion

The only scenario that fits the parameters provided is that Sam saw 14 movies, leading to Lucy watching 7 movies. This configuration results in a range of 10 when compared to the highest and lowest movie counts among all individuals involved. Hence, option A is the only valid answer.

Sam could have seen 14 movies last year.

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