A prize of $500 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?  Choose the correct choice from the following answers: A) $ 160 B) $ 220 C) $ 280 D) $ 300 E) $ 360

Rationale: total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer .
Answer: A