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?

Solution

let's assume there are n persons at the party.

Since everyone gives a gift to everyone else, the number of gifts exchanged is the number of pairs of people.

Each person gives a gift to n-1 other people, so the total number of gifts exchanged is:

So, total gifts: n * (n-1)

We know:

n * (n-1) = 600

Now, using options, we see that n = 25 satisfies the condition.

Hence, there were 25 people at the party.

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