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GPREP question

by anjaligeorge1 » Thu Jun 05, 2008 8:15 pm
In a survey of students ,each student selected from a list of 12 songs 2 songs hat the student liked the best .If each song was selected 4 times , how many students were surveyed

96
48
32
24
18
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by kishore » Thu Jun 05, 2008 8:49 pm
In a survey of students ,each student selected from a list of 12 songs 2 songs hat the student liked the best .If each song was selected 4 times , how many students were surveyed

Answer: 24

Total Number of Songs = 12

Each student selects 2 songs

Each of the 12 songs are selected 4 times => 12 * 4 = 48 songs

Total students surveyed = Total songs / No. of selected songs by each

= 48 / 2 = 24
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by poseid101 » Wed Jan 13, 2010 2:17 am
got this problem wrong and was confused by "selection" out of X choices... to understand other variants of the problem, see "selection" in https://www.wolframalpha.com/input/?i=selection

calculating backwards: 24 students select 2 songs = 48 songs are selected, when we have 12 different songs, we will get 4 selections per student, so the number 24 works
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by ozlemmetje » Wed Feb 19, 2014 7:13 am
Hello,

I somehow do not understand the mentality here.

If each song was selected 4 times. How can that mean that there were in total 12x4=48 selections?

Can someone explain this to me in a simpler example? I really want to understand the mentality..

Thanks
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by Brent@GMATPrepNow » Wed Feb 19, 2014 7:19 am
ozlemmetje wrote:Hello,

I somehow do not understand the mentality here.

If each song was selected 4 times. How can that mean that there were in total 12x4=48 selections?

Can someone explain this to me in a simpler example? I really want to understand the mentality..

Thanks
Song A was selected 4 times
Song B was selected 4 times
Song C was selected 4 times
.
.
.
Song L was selected 4 times

So, the total number of selections = 4+4+4+4....(12 times) = 48
Each student selected 2 songs each
So, the number of students = 48/2 = 24

Does that help?

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by Brent@GMATPrepNow » Wed Feb 19, 2014 7:26 am
ozlemmetje wrote:Hello,

I somehow do not understand the mentality here.

If each song was selected 4 times. How can that mean that there were in total 12x4=48 selections?

Can someone explain this to me in a simpler example? I really want to understand the mentality..

Thanks
Actually, here's another way to look at it.
Pretend that we have a bowl for each song.
Students are given 2 marbles each, and they must place the two marbles in the bowls representing their favorite songs.

Bowl #1 receives 4 marbles
Bowl #2 receives 4 marbles
Bowl #3 receives 4 marbles
.
.
.
Bowl #12 receives 4 marbles

So, in TOTAL, the number of marbles = 4+4+4+4+.. (12 times) = 48
So, 48 marbles were distributed and EACH STUDENT gave out 2 marbles.

So, the number of students = 48/2 = 24

Cheers,
Brent
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by GMATGuruNY » Wed Feb 19, 2014 7:38 am
anjaligeorge1 wrote:In a survey of students ,each student selected from a list of 12 songs 2 songs hat the student liked the best .If each song was selected 4 times , how many students were surveyed

96
48
32
24
18
An alternate approach is to PLUG IN THE ANSWERS, which represent the number of students.

Answer choice C: 32
Since each of the 32 students makes 2 selections, the total number of selections = 32*2 = 64.
Since each song is selected 4 times, the total number of songs = (total number of selections)/(number of times each song is selected) = 64/4 = 16.
For 32 students, 16 songs are required.
Since the problem states that there are only 12 songs, the correct answer choice must be smaller.
Eliminate A, B and C.

Answer choice D: 24
Since each of the 24 students makes 2 selections, the total number of selections = 24*2 = 48.
Since each song is selected 4 times, the total number of songs = (total number of selections)/(number of times each song is selected) = 48/4 = 12.
Success!

The correct answer is D.
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by ozlemmetje » Wed Feb 19, 2014 8:04 am
I still cannot visualize it really. Sorry..:(

Is it 48 songs or 48 selections like (song 1, song2) ??
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by Abhishek009 » Wed Feb 19, 2014 9:27 am
ozlemmetje wrote:I still cannot visualize it really. Sorry..:(Is it 48 songs or 48 selections like (song 1, song2) ??
anjaligeorge1 wrote:In a survey of students ,each student selected from a list of 12 songs 2 songs hat the student liked the best .If each song was selected 4 times , how many students were surveyed
Give special emphasis to the red highlighted Part , we do not have any information about the number of students surveyed.

Let the Number of students surveyed be S

Further read the blue highlighted part , it states that each students selected 2 songs.

So the total Number of selections ( Irrespective of the Choice of Songs , Ie there is a possibility that two students might have the same preference for songs ) is -

2S

Next concentrate on the Orange highlighted part it states that each song was selected 4 times , so the total Number of selections of the 12 songs is -

12 X 4 => 48 Selections .


Now we know can say -

2S = 48

Or, S = 24


Hence Number of students surveyed is 24....
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by ozlemmetje » Wed Feb 19, 2014 9:40 am
Hi,

so in this context what is meant with selection is not 48 different groups like(song1, song2),(song1, song3)... etc. but the total number of selected songs, right?

Abhishek009 wrote:
ozlemmetje wrote:I still cannot visualize it really. Sorry..:(Is it 48 songs or 48 selections like (song 1, song2) ??
anjaligeorge1 wrote:In a survey of students ,each student selected from a list of 12 songs 2 songs hat the student liked the best .If each song was selected 4 times , how many students were surveyed
Give special emphasis to the red highlighted Part , we do not have any information about the number of students surveyed.

Let the Number of students surveyed be S

Further read the blue highlighted part , it states that each students selected 2 songs.

So the total Number of selections ( Irrespective of the Choice of Songs , Ie there is a possibility that two students might have the same preference for songs ) is -

2S

Next concentrate on the Orange highlighted part it states that each song was selected 4 times , so the total Number of selections of the 12 songs is -

12 X 4 => 48 Selections .


Now we know can say -

2S = 48

Or, S = 24


Hence Number of students surveyed is 24....
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by GMATGuruNY » Wed Feb 19, 2014 9:40 am
ozlemmetje wrote:I still cannot visualize it really. Sorry..:(

Is it 48 songs or 48 selections like (song 1, song2) ??
Make the problem visual.
Let the 12 songs be A, B, C, D, E, F, G, H, I, J, K, L.
Assign 2 songs to each student, using each song a total of 4 times.
Look for a PATTERN.

AB
AB
AB
AB
4 students so far.

CD
CD
CD
CD
Another 4 students.

Notice the pattern.
Each pair of songs corresponds to 4 students.
Thus:
AB --> 4 students
CD --> 4 students
EF --> 4 students
GH --> 4 students
IJ --> 4 students
KL --> 4 students
Total students = 4+4+4+4+4+4 = 24.

The correct answer is D.
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by Abhishek009 » Wed Feb 19, 2014 10:08 am
ozlemmetje wrote:Hi,

so in this context what is meant with selection is not 48 different groups like(song1, song2),(song1, song3)... etc. but the total number of selected songs, right?
Yup absolutely...

Check Gmatgrunny's Visual Representation.

AB --> 4 students
CD --> 4 students
EF --> 4 students
GH --> 4 students
IJ --> 4 students
KL --> 4 students

Each song is selected 4 times....
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by feedrom » Thu Feb 20, 2014 8:56 am
"Each student selected from a list of 12 songs 2 songs":

so, if each song was selected 1 time --> 6 students
If each song was selected 4 times --> 6x4 =24 students
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