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?

Solution:

(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)**

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