10.10.20.0/24 must be divided using VLSM to provide subnets for 120 hosts, 30 hosts, and 6 hosts. Which prefix length should be assigned to the subnet that needs to support 120 hosts?

To accommodate 120 hosts, we need a subnet that provides at least 122 usable IP addresses (120 for hosts, 1 for network, 1 for broadcast). A /25 prefix provides 2^(32-25) = 2^7 = 128 total IP addresses. After subtracting the network and broadcast addresses, this leaves 126 usable host addresses, which is sufficient for 120 hosts. A /24 prefix provides 254 usable hosts, which is more than necessary and would waste IP addresses. A /26 prefix provides only 62 usable hosts, which is insufficient for 120 hosts. A /27 prefix provides only 30 usable hosts, also insufficient. Therefore, /25 is the most efficient prefix length that meets the requirement.