"You have configured a new VPC with a private subnet and added a NAT Gateway and configured the subnet route table to route all internet traffic via the NAT Gateway. However when you try to run a yum update, none of your instances are able to reach the internet. What could be the problem?"
I read this as there is only a private subnet where the NAT Gateway has been put into. That will never work because NAT Gateways should be in public subnets (subnets attached to IGW). Please enhance this question a bit so it reflects the actual situation.
I’ll take a look at the question and see if it needs a clarification,
It doesn’t need any further clarification because if this logic would be followed then the configuration of the subnet route table to route all internet traffic via the NAT Gateway would also take place within the subnet. That is not possible and quite funny if we try to imagine this. Whoever wrote this was not trying to be humorous!
I agree, it sounds like the NAT Gateway was added to the private subnet. It should be re-formulated a bit to clarify that there is also a public subnet.