N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?  Choose the correct answer
A) 5  B) 7  C) 9  D) None  E) Cannot be determined
Explanation :   Each person sings with everyone else other than the ones standing near him and “himself”.   So, each person sings with (n-3) persons. Also, they stand in form of a circle, so we can avoid 1 side of the circle, as all the others would have already sung.   Total number of songs, hence is n * (n – 3 ) / 2.   Total song time = 28 minutes, and 2 minutes per song.   So, total number of songs is 14.   So, n*(n – 3) / 2 = 14. n*(n-3) = 28 =&gt; n = 7.   Answer : 7
<result>B</result>
N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?