CCNA Exam: Subnet vs Host

And ..

Here's the answer:

http://www.allinterview.com/showanswers/81827.html

Check it out.

Number of subnets would be 16 2*2*2*2, number of hosts per subnet would be 2 to the power n -2 that is 32-2 = 30

Since I'm not a fan of clicking on links to get answers (it's not that I don't trust you, but...).  Here is the deal:
172.17.32.0/23 is the address space you start with and represents 2^(32-23) ip addresses - or 2^9=512 addresses (including network and broadcast addresses).  Or you can say you have ONE subnet with 510 hosts

If you split this address space in two using a /24 mask, you get two subnets, which equates to one **extra** subnet (2-1=1), therefore you **gain** one subnet. Each subnet will have 254 hosts (2^8-2)

If you split these two subnets again, you end up with 4 subnets with a /25 mask, giving you 4 subnets, so a **gain** of 3 subnets.  Each subnet has 126 (2^7-2) hosts.

If you split these two subnets again, you end up with 8 subnets with a /26 mask, giving you 8 subnets, so a **gain** of 7 subnets.  Each subnet has 62 (2^6-2) hosts.

If you split these two subnets again, you end up with 16  subnets with a /27 mask, giving you 16 subnets, so a **gain** of 15 subnets.  Each subnet has 30 (2^5-2) hosts.

So the **CORRECT** answer is that you **gain** 15 subnets (remember you had 1 to start with, and you haven't lost it) and each subnet has 30 hosts.

If the CORRECT answer is not available for a given question, you have to guess what the examiner thinks is the "most correct" - in this case the idiot who set the exam probably couldn't count the original subnet you started with, so 16 subnets, each with 30 usable addresses is probably the best answer.

The multiples 2, 4, 8 , 16, 32, 64, 128 (and 256, 512, 1024 ...) come up time and time again in subnetting, so it is worth learning your 2, 4, 8 , 16, 32, 64, and 128 times tables - as far as 256 anyway.  Pretty soon you can work out that:
subnets that have a mask of /30 ALL start with a multiple of 4 (0, 4, 8, 12, 16, ...)
subnets that have a mask of /29 ALL start with a multiple of 8 (0, 8, 16, 24, 32, ...)
subnets that have a mask of /28 ALL start with a multiple of 16 (0, 16, 32, 48, 64, ...)
subnets that have a mask of /27 ALL start with a multiple of 32 (0, 32, 64, 96, 128, ...)
subnets that have a mask of /26 ALL start with a multiple of 64 (0, 64, 128, 192)
subnets that have a mask of /25 ALL start with a multiple of 128 (0, 128)
subnets that have a mask of /24 ALL start with a multiple of 1 (0, 1, 2, 3, 4, ... - in the 3rd octet)
subnets that have a mask of /23 ALL start with a multiple of 2 (0, 2, 4, 6, 8, ... - in the 3rd octet)
subnets that have a mask of /22 ALL start with a multiple of 4 (0, 4, 8, 12, 16, ... - in the 3rd octet)
and so on.  If you look at the mask in decimal, there is a formula to work out the multiple I've used above.  It is 256-(the last non-zero octet of the mask).  So if the mask is /19 aka 255.255.224.0, the multiple for your subnets is 256-224=32 - in the 3rd octet.  So you your subnets will be x.x.0.0, x.x.32.0, x.x.64.0, x.x.96.0 etc