In a party everyone gave a gift to everyone else. If the total number of gifts exchanged in the party was 600, how many persons were there in the party?

Options

A. 20
B. 15
C. 10
D. 25

Answer

D

Explanation

Let the total number of persons in the party = n
Then, total number of gifts exchanged in the party `= n(n-1)`.
According to the question `n(n-1) = 600 `
or, `n^2- n = 600 `
or, `n^2 - 1 - 600 = 0 `
Or, `n^2 - 25n +24n - 600 = 0 `
or, `n(n-25) + 24(n – 25) = 0`
or, `(n – 25) (n + 24) = 0 `
or, `n = 25 and n = 24 `
But, `n=-24 ` is rejected
[`because` No. of persons can.t be negative]
So, `n= 25` .
Therefore, the total number of persons in the party `= n = 25`