GATE CS 2022 Q.55: IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT

Consider routing table of an organization’s router shown below:

Subnet Number	Subnet Mask	Next Hop
12.20.164.0	255.255.252.0	R1
12.20.170.0	255.255.254.0	R2
12.20.168.0	255.255.254.0	Interface 0
12.20.166.0	255.255.254.0	Interface 1
default		R3

Which of the following prefixes in CIDR notation can be collectively used to correctly aggregate all of the subnets in the routing table?

12.20.164.0/20

12.20.164.0/22

12.20.164.0/21

12.20.168.0/22

Official answer and solution

Official answer: B and D
From: Official GATE 2022 answer key

Solution

Identify the IP address ranges of each subnet and combine them into minimal CIDR supernet blocks.

Let us determine the IP ranges for each subnet in the routing table:

12.20.164.0 / 255.255.252.0 (/22): Covers third octet range $164$ to $167$ (12.20.164.0 - 12.20.167.255).
12.20.166.0 / 255.255.254.0 (/23): Covers third octet range $166$ to $167$ (this is already subsumed within the /22 above).
12.20.168.0 / 255.255.254.0 (/23): Covers third octet range $168$ to $169$ (12.20.168.0 - 12.20.169.255).
12.20.170.0 / 255.255.254.0 (/23): Covers third octet range $170$ to $171$ (12.20.170.0 - 12.20.171.255).

Together, the entries span third octet values from $164$ to $171$ (8 contiguous /24 blocks):

The range $164..167$ has binary prefix 101001xx, which forms the /22 prefix 12.20.164.0/22 (Option B).
The range $168..171$ has binary prefix 101010xx, which forms the /22 prefix 12.20.168.0/22 (Option D).

Together, 12.20.164.0/22 and 12.20.168.0/22 precisely cover the entire set of subnets without including any outside addresses. Hence, Options (B) and (D) collectively aggregate all subnets.

Final answer

Options (B), (D)

Common trap

Aggregating into 12.20.164.0/21, which is not aligned on an 8-block boundary (a /21 starting at 164 is invalid because 164 is not divisible by 8).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2022 Computer Science and Information Technology (CS)
Question: 55 of 65
Section: Computer Science and Information Technology

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