Question

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?

• A. 20
• B. 15
• C. 10
• D. 25

Answer 1

Answer: (D)

25

Answer 2

Each person gives a gift to every other person, so the formula is:
$\text{Total gifts} = n(n-1)$
where $n$ is the number of people
$n(n-1) = 600$
$n^2 - n - 600 = 0$
Use the quadratic formula:
$n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Here, $a = 1$, $b = -1$, $c = -600$.
$b^2 - 4ac = 1 + 2400 = 2401$
$n = \frac{1 \pm 49}{2}$
$n = \frac{50}{2} = 25$ (positive solution)
$n = \frac{-48}{2} = -24$ (not valid)

There were 25 persons at the party.