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

The Correct Option is D

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.