Grr... I will now clear this up once and for all (though I usually explain this at least once a week).
The GE's minimum price will not necessarily sell it for the minimum. Think of it as an auction, where the minimum price is the starting price, but where there is a price cap (the maximum price). If item A has a market price of 90-110gp, and you sell it at the minimum (90), but someone is trying to buy at max price (110), it will sell at 110. But if people are only buying at min price (90), the best offer there is is 90gp, thus that's what you'll get.
This applies to buying too, so offering the max price when buying will give you better chances of getting that item, abet, you will always spend all that money. If you have the time, you can try buying at the min price, if that doesn't buy, you can try the market price, then lastly, the max price. That is good only for when there is plenty of stock, and you want to save the money (or can't scrape up the money, such as to buy expensive items like the Whip).
I hope that is understandable.