P&C-7 (CAT-2004)

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?

(1) 5

(2) 7

(3) 9

(4) None of these

For Answer Click on "Read more" below:

Solution:

Let us check from the answer options:

Point here is “we should not consider a pair of two adjacent persons”

Option(1)      5 members on a circle:

The possibilities of A pairing with:    AC, AD

The possibilities of B pairing with:    BD, BE

The possibilities of C pairing with:    CE  (AC -already considered above)

Total possible pairs = 2+2+1 = 5

Total time taken by 5 pairs = 2*5 = 10 minutes => this option is wrong

Option(2)      7 members on a circle:

The possibilities of A pairing with:    AC, AD, AE, AF

The possibilities of B pairing with:    BD, BE, BF, BG

The possibilities of C pairing with:    CE, CF, CG (AC- already considered above)

The possibilities of D pairing with:    DF, DF (AD,BD- already considered above)

The possibilities of E pairing with:    EG (AE,BE,CE- already considered above)

Total possible pairs = 4+4+3+2+1 = 14

Total time taken by 5 pairs = 2*14 = 28 minutes => this option is correct

Answer (2)