Why does GOD let the poor suffer and die, while the greedy rich people live a happy life?
I believe your question is more in line with why does it seem like people who are not well off financially go through the things they do, suffering financially etc. when it appears that others who are in a better financial state and don't appreciate it seem to have a care free life. God is in control of everything that happens; good, bad or indifferent. People who are wealthy and have a greedy attitude towards money, prosperity etc will eventually have to come to terms with themselves. God says, these people have their reward and inevitably they will run into problems, because material possessions are no substitute for the Grace of God;
"But they that will be rich fall into temptation and a snare, and into many foolish and hurtful lusts, which drown men in destruction and perdition." 1 Tim. 6:9
It always seems like the rich get richer and the poor get poorer. But one thing the believer in Jesus has that the unbeliever, or those that value wealth and this life more than Him does not have is the grace of God, the comfort knowing, no matter what, He is with us in all of our trials. This is not to say that all people that have wealth are selfish or greedy. There are a lot of very caring people who honestly worked hard to get to where they are and there's nothing wrong with that. These are the ones who truly care and do in fact help the needy. God knows the truth of our hearts. No amount of money or material possessions can out value the need for God. Those that are the 'rich greedy' type you talk about, Jesus convicted them in the book of Luke;
"And the Lord said unto him, Now do ye Pharisees make clean the outside of the cup and the platter; but your inward part is full of ravening and wickedness." Luke 11:39
Understand that what others do or have should not be ones major concern. Your belief in God through our Lord and Savior Jesus Christ will give you all that you need in life........ All of the other material wealth issues are nothing in comparison.