M40-123

Question

Marcus owns a movie collection consisting 160 movies, each of them is either a comedy, action movie, or both. He has watched 25% of the comedies and 60% of the action movies. What percentage of the entire collection has Marcus watched?

(1) Marcus owns 80 comedies.

(2) Marcus owns 120 action movies.

Show Answer

Official Answer

E

(1) Marcus owns 80 comedies.
 
(2) Marcus owns 120 action movies.

Bunuel · Answer

Official Solution:

Marcus owns a movie collection consisting 160 movies, each of them is either a comedy, action movie, or both. He has watched 25% of the comedies and 60% of the action movies. What percentage of the entire collection has Marcus watched? 
 
(1) Marcus owns 80 comedies.
 
This allows us to calculate how many comedies he has watched (25% of 80 = 20), but we still cannot determine the total number of movies he watched. Not sufficient.
 
(2) Marcus owns 120 action movies.
 
This allows us to calculate how many action movies he has watched (60% of 120 = 72), but we still cannot determine the total number of movies he watched. Not sufficient.
 
(1)+(2) We can determine that 80 + 120 - 160 = 40 movies are categorized as both a comedy and an action movie. We also know that Marcus watched 20 comedies and 72 action movies. However, some of the movies he watched may fall into both categories, meaning they could have been counted twice. Without knowing how many of the watched movies overlap, we cannot determine the total number of distinct movies he has watched. Therefore, we cannot calculate the percentage of the 160 movies he watched. Not sufficient.
 
Answer: E

Pranavsawant · Answer

I think we might wanna update the difficulty level  Bunuel  
This is a lot trickier than it seems.

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined automatically based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question.

Adit_ · Answer

It is tricky agreed but the whole point is to notice that:
1)We need categories where he watched both
2) Either 1 is clearly insufficient. Combining the two we only know HOW MANY movies are there and we still dont know how many cases have movies where BOTH are WATCHED.

The entire trick being, data is given as:
1) No.of movies THERE
2) Question: Movies he watched 
And from nowhere in the stem or the statements after a quick glance we find any mention of how many of the movies he watched of BOTH types. Hence without any calculation we can safely proceed with E.

M40-123

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