How can I enable outgoing HTTP/HTTPS requests on an EC2 in a public subnet within a VPC on Amazon AWS

Why doesn’t the provided AWS DNS Server work in this case?

PROBLEM

The problem was that DNS names weren’t resolving via the local DNS server than Amazon provided when originally creating the VPC. I discovered that I could make outgoing HTTP/HTTPS connections to IP addresses, which didn’t need to contact a DNS server to resolve.

SOLUTION

I had to create a custom DHCP Option Set within the Amazon VPC AWS Console and set Google’s public DNS IPs as domain-name-servers = 8.8.8.8, 8.8.4.4.

Then I had to update /etc/resolv.conf setting the same thing: 
nameserver 8.8.8.8
nameserver 8.8.4.4