Question

At a conference, every member attending the event makes a handshake with every other member. If there were 105 handshakes in all, what was the number of members attending the conference?

• A. 15
• B. 14
• C. 13
• D. 16
• E. 20

Answer 1

The correct option is A

15

Let there be $x$ member attending the conference.
So,
$\frac{x(x-1)}{2}-12=105$
$x^2-x=210$
$x^2-x-210=0$
$x^2-15x+14x-210=0$
$x(x-15)+14(x-15)=0$
$(x-15)(x+14)=0$
$\therefore x=15,-14$ But -ve sign is ignored
So,
$x=15$