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LOGIC questions from "getting into oxbridge guide"

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LOGIC questions from "getting into oxbridge guide"

Ok people, these are some of the logic questions from the "getting into oxbridge for social sciences" guide which i need help with. There are quite a few so what i am going to do is post them individually then we can discuss solutions before posting the nest question. For some of them, i'm not even sure if there is a "CORRECT" answer! Anyway here goes with the first:

You are thinking of buying a second-hand car. You are prepared to pay £5000 for a good car, but only £1000 for a bad car. You do not know where the car which you are buying is in good or bad condition. However you believe that a quarter of the cars on the road are good and three quarters are bad.
(a) What is the expected value of the car to you?
(b) How much would you offer for the car? (no right or wrong answer so justify reasoning for answer)
(c) You know that the seller of a good car will only sell for a minimum of £4000, while a seller of a bad car will sell for a minimum of £500. What would you now offer for the car? (assume there are laws which make all bids binding, so they cannot be cahnged once an offer is accepted)
(d) How might the seller of the second hand car convince the buyer of the high quality?