Refusing to repair

I bought a used car over a month ago at the dealership and I was told it has a new engine, they lost the service book and I could not get my own after market warranty that I could afford and they were basically forcing me to get their warranty which I refused to get,because I could not afford it, now the water pump has went and they are telling me it is my responsibility to fix it 41 days after delivery, is this my responsibility?