ANSWER: You ask a fascinating question that also puzzled Jesus' disciples. Their inquiry was generated when a rich young ruler came to him seeking to know what it took to receive eternal life (be saved). We find the account in the books of Matthew (19:16 - 26), Luke (18:18 - 27) and Mark (10:17 - 27).
And a certain ruler (who was both rich (verse 23) and young (Matthew 19:20) asked Him, saying, "Good Master, what shall I do to inherit eternal life (be saved forever)?" (Luke 18:18, HBFV)
The man was zealous to know about the Messiah and be saved. In addition, even though he was rich, he was not overtly arrogant or self-righteous like the Pharisees or other religious leaders. The book of Mark states that the rich man not only ran toward Jesus but also knelt humbly in front of him before asking his question (Mark 10:17)!
Christ's response (which is one proof refuting the silly notion that Jesus came to do away with God's laws) was to tell the rich gentleman he needed to keep the last six of the Ten Commandments (Matthew 19:17 - 19). These commandments center on how humans are to treat one another.
The rich man then stated he had kept these commandments since he was young. His character so impressed the Lord that the Bible says he loved him (Mark 10:21). Jesus then fully revealed to him what he still lacked in order to be one of his disciples and saved.
The wealthy person who spoke to Jesus needed to abandon his love of money, sell all he had, give the money to the poor and follow the ways of righteousness (Mark 10:21). The young man, sadly, rejected what he was told because he did not want to give up being rich with all the worldly benefits it generated (Matthew 19:22).
The man kept the letter of God's laws but refused to keep their spiritual intent. He had made being rich into an idol or god in his heart, which broke the spiritual intent of the first two commandments (Exodus 20:3 - 6). Such idolatry interfered with his relationship with God. He loved what the world had to offer more than what Jesus could give him.
Christ then told his disciples it was incredibly difficult for those who are wealthy to enter God's Kingdom. To illustrate his point, he gave a parable about how hard it was for a camel to go through the eye of a needle. The disciples were astonished and dumbfounded at his answer and asked, "Who then is able to be saved?" (Matthew 19:25, Luke 18:26). His answer was that all things were possible with God (Matthew 19:26).
Abraham, the father of the faithful, was rich in his day. Abraham not only possessed wealth in animals and people, he also owned quite a bit of gold and silver (Genesis 13:2). Daniel and Job, whom God considered two of the three most righteous people who ever lived (Ezekiel 14:14), also were quite prosperous.
Yes, it is possible for the rich to be saved! Those who are wealthy, however, must always place obedience to the Eternal and a relationship with him first in their lives if they want to receive the gift of salvation.