You have Class B network 134.57.0.0 and need subnets that each support at least 600 hosts. To maximize the number of subnets while meeting this host requirement, which mask should you assign (choose from the options provided)?

Introduction:
For a Class B block (default /16), choosing a subnet mask requires balancing the number of hosts per subnet against the number of available subnets. The goal here is to meet at least 600 hosts per subnet while maximizing the number of subnets given the answer choices provided.

Given Data / Assumptions:

• Base: 134.57.0.0 (Class B, /16).
• Required hosts per subnet: ≥ 600.
• We must pick from the listed masks only.

Concept / Approach:
Hosts per subnet = 2^(host_bits) - 2. To support ≥600 hosts, host_bits must be at least 10 (2^10 - 2 = 1022). That implies a /22 prefix (since 32 - 22 = 10). A /22 mask is 255.255.252.0, which would maximize subnets while meeting the host requirement. Although /22 is not offered in the options, the next longest prefix among the choices that still satisfies ≥600 hosts is /21 (255.255.248.0) with 2^(11) - 2 = 2046 hosts per subnet. /21 yields more subnets than /20 or /19, and /24 is too small for 600 hosts.

Step-by-Step Solution:
1) Compute minimum host bits: need ≥600 → host_bits = 10.2) Ideal mask: /22 (255.255.252.0) → not in options.3) Choose longest available prefix that still meets hosts: /21 (255.255.248.0).4) Validate: 2046 hosts/subnet ≥ 600; more subnets than /20 or /19.

Verification / Alternative check:
Check other options: /24 (254 hosts) fails; /19 and /20 allow many hosts but fewer subnets than /21, contradicting the “maximize subnets” goal.

Why Other Options Are Wrong:

• 255.255.224.0 (/19) and 255.255.240.0 (/20): satisfy hosts but yield fewer subnets than /21.
• 255.255.255.0 (/24): only 254 hosts; insufficient.
• 255.255.255.255 (/32): no host capacity.

Common Pitfalls:
Forgetting that to maximize subnets you choose the longest allowable prefix that still meets the host requirement; if the ideal mask is missing from options, select the closest longer prefix that remains valid.

Final Answer:
255.255.248.0