The 400 seats in a parliament are divided amongst five political parties. No two parties have the same number of seats, and each has at least 20 seats.

What is the largest number of seats that the third largest party can have??

A 22

B 118

C 119

D 120

E 121

Also, kindly specify your technique for solving this kind of question.

Hi!

The following parties are:

A ; B ; C ; D ; E

20 ; 20 ; 20 ; 20 ; 20 seats

All number of seats must be different, and we want C to be as big as possible, so A and B have to be as small as possible

A ; B ; C ; D ; E

20+0 ; 20+1 ; 20 ; 20 ; 20

We now have 300-1=299 seats to divide among C D and E

299/3 = 99 + remainder of 2

The best configuration to have C as big as possible is:

A ; B ; C ; D ; E

20 ; 21 ; 20+98 ; 20+100 ; 20+101

So C=118

Is this the correct answer?