Latest Athenahealth Aptitude Question SOLUTION: n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken

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n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n

Asked In Athenahealth karthik (9 years ago)

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Sreeram  (9 years ago)

n=7; i.e 7 people there.
1st person sing with 3,4,5 and 6 (singing time 8 min as it take each song 2 min) means 2 and 7 were adjacent to him.
2nd person sing with 4,5,6 and 7(singing time 8 min) means 1 and 3 were adjacent to him. (total singing time so far is 16 min).
3rd person will sing with 5, 6 and 7(singing time 6 min) as he has already sang with 1. Also 2 and 4 were adjacent to him.(total singing time 22 min so far).
4th person will sing with 6 and 7(singing time 4 min). (total singing time 26 min so far).
5th person will sing with only 7(singing time 2 min). (total singing time 28 min).
6 and 7th persons will not sing anymore as they had already sang with every possible person(see the above singing data) (so total singing time is 28 min)

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deepak  (9 years ago)

each of 2 present in the party =>no. of pairs possible=nc2
possible adjacent pairs=n
total required combinations=nc2-n
time taken by each combination to sing a song=2 min
total time taken=2(nc2-n)=28
on solving the above equation, we get n=14

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Daniel  (9 years ago)

If the people facing opposite to each other sang the song for 2 min, then it would take 14 such pairs to sing for 28 min. which tells us that there were 28 people. ( this is valid if repetition is not allowed)

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Sarabeshwar  (9 years ago)

14 min..............sure

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monish kumar  (8 years ago)

n people sitting in a circle.
a person makes pair with all except his adjacent one.
total song lasted for 28min and each song is 2min
therefore 14 songs are sang.
15 persons are required to form 14 pairs.
he does not pair with the person sitting adjacent to him.so +1
therefore 16 =n.

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jayagopi  (9 years ago)

@Deepak Your approach is correct . But ans wrong . nC2-n=14 and if u solve it u will get n=7

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Kannan Mohan  (8 years ago)

ANS : 7
2 sang one song for 2 minutes .
Total number of pairs = 28/2=14 pairs
If there are 3 people and they sit on a circular manner then no pair formed so 3 people =0
4 people ABCD . Then pairs are AC and BD = 2 pairs
5 people ABCDE . Then pairs are AC,AD,BD,BE,CE = 5 pairs
6 people ABCDEF . Then total pairs = 9 pairs

It goes in order 0,0,0,2,5,9,14 .. So 7 people!

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