A network administrator is adding a new LAN to a branch office. The new LAN must support 25 connected devices. What is the smallest network mask that the network administrator can use for the new network?

To support 25 devices on a network, you need to have at least 25 available IP addresses for the devices, plus one for the network address and one for the broadcast address.

The subnet mask that can provide at least 27 addresses (25 for devices, 1 for the network, and 1 for broadcast) is a /27 subnet mask. This is because:

• A /27 subnet mask has 5 bits available for host addresses (32 – 27 = 5).
• With 5 bits, you can have 2525 or 32 possible combinations.
• Subtracting 2 for the network and broadcast addresses leaves you with 30 usable IP addresses.

The subnet mask 255.255.255.224 corresponds to a /27 subnet mask, which supports up to 30 usable IP addresses, which is sufficient for 25 devices.

So, the smallest network mask that the network administrator can use for the new network to support 25 connected devices is 255.255.255.224.