Question

In a party, everyone gave a gift to everyone else. The total number of gifts exchanged in the party was 600.
How many persons were present in the party?

• A. 20
• B. 15
• C. 10
• D. 25
• E. 30

Answer 1

The correct option is D

25

Let there be $x$ persons in the party.
$x(x-1)=600$
$x^2-x-600=0$
$x^2-25x+24x-600=0x(x-25)+24(x-25)=0(x-25)(x+24)=0$

$\therefore$ $x$ = 25 or $x$ = -24 (But -ve sign is ignored)
So, $x$ = 25