Question 17

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?

[CAT 2004]

Solution

Total number of pairs is $$^{N}C_2$$. Number of pairs standing next to each other = N. Therefore, number of pairs in question = $$^{N}C_2$$ - N

= 28/2 = 14.

If N = 7,

$$^{7}C_2$$ - 7 = 21 - 7 = 14.

N = 7.

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CAT 2004 QA Question

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? [CAT 2004]

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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?

[CAT 2004]