A hundred students of Midtown college were asked

Question

A hundred students of Midtown college were asked to pick their preference for one of three genres of movies: romantic, drama, and tragedy. Each of them picked one of the three genres. More than half picked romantic, more than a quarter picked drama and at least one picked tragedy. When asked about the genre of the movie Titanic, however, more than three quarter viewed it as a romantic movie.

If all of the statements above are true, which one of the following must also be true?

A: Only the students whose preferences were romantic and drama genres of movies viewed Titanic as a romantic movie.
B: Only the students whose preferences were romantic and tragedy genres of movies viewed Titanic as a romantic movie.
C: At least one student from each genre of movies viewed Titanic as a romantic movie.
D: Some students whose preference was romantic genres of movies viewed Titanic as a romantic movie.
E: Some students whose preference was tragedy genres of movies viewed Titanic as a romantic movie.

ajaygaur319 · Accepted Answer

Total number of students: 100
According to the statement, let's assume:

The total number of students who had preferences for romantic movies: 51
The total number of students who had preferences for Drama movies: 26
The total number of students who had preferences for Tragedy movies: <= 23

A: Only the students whose preferences were romantic and drama genres of movies viewed Titanic as a romantic movie. -  We cannot say that because someone who prefers tragedy might have viewed as romantic 
B: Only the students whose preferences were romantic and tragedy genres of movies viewed Titanic as a romantic movie. -  Romantic + Tragedy = 74 but three quarters (75) viewed it as a romantic movie. Cannot be true 
C: At least one student from each genre of movies viewed Titanic as a romantic movie. -  Romantic + Drama = 76. It might happen that only such people watched this movie and termed that romantic 
D: Some students whose preference was romantic genres of movies viewed Titanic as a romantic movie. -  True, at least a few people must have thought Titanic as Romantic because Drama + Tragedy = 49 and to make 75, some people from romantic genre must've seen this as romantic 
E: Some students whose preference was tragedy genres of movies viewed Titanic as a romantic movie. -  Doesn't have to be true because rest 2 can have a sum of 76

(D)  is the correct answer.

TheProfessor99 · Answer

@  nightblade354

RENIS · Answer

We know that 100 people have chosen. Let's say,
R=55 
D=30
T=15
>3/4 picked R, let's say 80 students.

Remember the keywords is "MUST BE TRUE"

Let's check the option:
A. Only Romantic and Drama
 It's true(for ex: R+D=50+30=80). But we have another possibility -> R+D+T=50+25+5. So, this statement isn't always true.

B. Only Romantic and Tragedy
It's not true(for ex: R+T=55+15≠80 or we can use another example, R+T=51+23≠76). So, this statement is absolute wrong.

C. At least one from each genre(Remember, not must at least, not be 1)
 We have many probability,
 1.)R+D+T=50+29+1
 2.)R+D+T=55+10+15
 3.)R+D=50+30 (Enough),...etc. So, this statement isn't always true.

D. Some Romantic.
It's absolute true. Because we know that D+T=30+15=45, which is it can't reach 80 student. So, we need 30 more students. 
 
E. Some Tragedy
It's true(for ex: R+D+T=50+25+5=80). But we must remember that just Romantic and Drama still enough (R+D=50+30=80). So, this statement isn't always true.

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sunil1999 · Answer

A: Only the students whose preferences were romantic and drama genres of movies viewed Titanic as a romantic movie.( what if the students whose preference is tragedy picked titanic as romantic, so we can rule out this )
B: Only the students whose preferences were romantic and tragedy genres of movies viewed Titanic as a romantic movie.( what if the students who picked drama viewed titanic as romantic, so we can rule out this  )
C: At least one student from each genre of movies viewed Titanic as a romantic movie.( not necessarily true, because students who preferred tragedy wouldn't add any value ,as students who picked romantic and drama are sufficient to cross the three quarter mark )
D: Some students whose preference was romantic genres of movies viewed Titanic as a romantic movie.( So obviously this makes us to believe it as the right answer cause it must be true  )
E: Some students whose preference was tragedy genres of movies viewed Titanic as a romantic movie.( goes in similar lines with option C  )

Sajjad1994 · Answer

Explanation

This is a kind of math + logic question.

We have 100 students, each picked one favorite movie type:

Romantic: at least 51 students (more than half)

Drama: at least 26 students (more than a quarter)

Tragedy: at least 1 student

Second fact:

When asked about Titanic, more than 75 students (so at least 76) said they see it as a romantic movie.

Key point:  If none of the students who prefer Romantic thought Titanic was romantic, then all 76+ people who see it as romantic would have to come only from Drama + Tragedy fans.

But Drama + Tragedy fans are at most

100−51=49 people (if Romantic-preferring students = minimum 51). So 76 people can’t come from a max of 49 people. Impossible! Therefore, at least some of the Romantic-preferring students must see Titanic as romantic.

That’s exactly what option D says.

Other options might be true in some case, but only D is guaranteed by the math even.

Answer: D

A hundred students of Midtown college were asked

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