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In the below given network, the source IP address is 10.1.1.10.

Suppose a host X with IP address 192.16.1.97 is connected through two routers R1 and R2 to another host Y with IP address 10.1.1.7. Router R1 has two IP addresses 192.16.1.135 and 192.16.1.110. Router R2 has two IP addresses 10.1.1.67 and 10.1.1.155. The network mask used is 255.255.255.224. Which IP address should X configure its gateway?

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Asthe subnet mask is 255 255 255 224 , i think 

gateway will be 192.16.1.110 ??

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R1 is connected with 2 IPs namely 192.16.1.135 and 192.16.1.110.  

X has IP address 192.16.1.97 with 192.16.1.011***** as network id in the last octet. So, the gateway should also have the same network id as 
192.16.1.011*****. 192.16.1.110 has the same Network ID and hence should be the gateway for X node.