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Correct approach to determine subnet mask

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Correct approach to determine subnet mask

bohlinsitsupport
Hi!

Studying for the Microsoft 70-291 exam: "Windows 2003 Network Infrastructure". Question 1 at page 8-37 states:
DHCP server must have IP address 207.46.47.150 and this server lease addresses to the local network segment through the scope of 207.46.48.0
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Which subnet mask can you assign to the server and scope that will place the DHCP server and clients on the same logical subnet and reserve the fewest number of bits possible for the host ID?

The way I went about this question was to test decreasing a C-class IP subnetmask (i.e. 255.255.255.0) by decreasing the third octed one bit at a time, and then AND:ing the third octet with 47 (third octet in DHCP static IP address) and 48 (third octet in DHCP client/lease addresses). Now, by testing with subnet masks 254, 252 etc all the way down to 224 I found that 224 would be the one. It is the correct answer.

I suspect this trial and error method of mine isn't optimal? Could anyone, please, suggest a smarter method?

Regards,

T