12 Parties

A logic test from a job selection process:

A nation’s people can vote for members of parliament from 12 parties. One voter must cast only one vote for one representative. If a party doesn’t get more than 5% of votes, then it won’t get any chairs in the parliament. How many chairs can get (at most) the party which collects 25% of votes?

Solution

1. If V1 == 25%, then Sum(Vi, i=2..12) == 75%

2. The best for P1 would be that the other parties get 5% of votes, so that they lower the 75% but don’t get any chairs.

   • 5% * 11 = 55% < 75%
     11 other parties cannot get 5% each because there are no parties left to absorb the remaining 20% of votes.

   • 5% * 10 = 50% -> V2 = 75% – 50% == 25%
     10 other parties can get 5% each instead because the remaining party can get the remaining 25% of votes.

3. Only P1 and P2 will share the parliament, and each of them with 50% of the chairs.