In a survey of students, each student selected from a list

I counted using pairs. Each pair 4 times. I ended up with 24. IS 24 correct?

I have 48, but I don't understand the logic of the question.

I don't think this is a gmatprep question either.

48 should be the minimum students surveyed, but the maximum students surveyed is unknown, since there is no guarantee that 4 people will pick a song as their favorite, even if you survey 100000000000000000 people.

yes it is confusing but not tough really:

considering 4 times that each song is repeated - the total number of songs selected is 48 but then each student selects 2 songs - thus the total number of students here must be 24 to the least.

The question stem is not right - it should day the least number of students required to get 4 as the number of times each song is selected!

It IS right.

It says that each song was selected 4 times. Not 5 or 6 or more.

Therefore exactly 4*12 = 48 choices have been made.

And since each student makes 2 choices, it means that 48/2 = 24 students were surveyed.

key word here is ..EACH SONG is chosen 4 times..

this means..that 4*12 =48 possibile students..however we are then told that each student chooses 2 songs..

so minimum number of students is 24..

and maximum number of students is 24 because each student chooses 2 songs.

If you are to "survey" people and each person pick 2 songs from a list of 12 songs. How do you ensure that each song is picked 4 times? The only way for that to happen is that you remove the songs from the list when they had been picked 4 times. But if that is the rule, the last person "surveyed" will be ask to pick 2 songs from a list of 2 songs. How is that a survey? What if the person does not like either songs?

It's not a matter of removing any songs. What the authors mean is essentially that at the end of the survey, it so happend that each song was picked exactly 4 times. Unrealistic, but since when was reality imposed on GMAT test authors?

Yes, that is the point, you can "survey" 10000000000000000000000000 people and there is no guarantee that 1 song will be picked 4 times. If one song sucks so bad, no one will pick it.

On the GMAT you just have to be able to accept that when the question reads "students were surveyed and each song was selected 4 times" that however many students there were, the survey resulted in every song being selected 4 times total. If you surveyed 100,000,000 students, sure you could get more than 4 songs, but you have to accept as fact the statements made in the question stems.

We could attack this survey on all types of angles.

Were the students allowed to abstain if they hated all 12 songs?
If they must vote, were they instructed to pick the 2 songs they disliked the least?
Were the students responses a result of leading questions?
Was there any type on control group with which to compare these results in order to determine if any bias exists among those surveyed?

We can think of all types of things that would be relevant to a survey, but in the end, we have to live in the GMAT world and only respond to what information is given and in the method it is provided.

Here, after the survey is complete, each song was selected 4 times. Thus, we know that 12 songs * 4 selections = 48 total selections / number of selections allowed per student = 24 students participated in the survey.

I don't ensure anything.

Each song WAS selected 4 times: this is the original statement of the question. To answer this question, I have to take it granted. Even if you think the event is unlikely, there is a chance it could happen and GMAT asks us to reason under that chance.

And no: the only way for that is that there are 24 students that took the survey. And each of the 12 songs was on the preferred list of 4 students (not more, not less).

Tricky -

here's an easy logic -

12 songs - 6 students - each song selected once
12 songs - 12 students - each song selected twice
12 songs - 18 students - each song selected thrice
12 songs - 24 students - each song selected 4 times

Since each of the 12 songs was selected 4 times, thus there were a total of 12 x 4 = 48 song selections. Since each student had 2 song selections, there must be 48/2 = 24 students.

Answer: D

Hi

I solved the question using the below approach.

There are 12 songs and each student had to choose two songs.
The number of combinations of two songs is \(12 C_{2}\) = \((12!)/(10! * 2!)\) = 66

In these 66 combinations, each song appears 11 times.
It is given that each song is chosen 4 times. Therefore, the number of combinations with each song repeating 4 times is \((66*4)/11\) = 24

The above number of combination of songs represents the number of students participated in the survey. Hence, 24 students participated in the survey.

Answer: D

amenon55,

Nice and easy explanation to the solution.

can you explain how do you say that 'In these 66 combinations, each song appears 11 times" ? Not able to understand where the 11 times comes from

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.