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The correct answer is supposed to be:
Correct Answer: RT3 has an IGP metric of 782 to reach 192.168.1.1

This answer makes no sense to me... perhaps you can help. 

In the routing table it states:

202.176.56.0 /24 [200/1782] via 192.168.1.1
200 = AD of IBGP
1782 = metric of IBGP correct?  Why is the answer not
RT3 has an IGP metric of 1782 to reach 202.176.56.0/24.

22. (QID:NF55) View the exhibit. Router RT3 discovers network 202.176.56.0 via BGP. Which one of these statements is true?

RT3 has an IGP metric of 1782 to reach 202.176.56.0/24.
RT3 has an IGP metric of 782 to reach 192.168.1.1.
RT3 has a BGP metric of 782 to reach 192.168.1.1.
RT1 advertised network 202.176.50.0/24 with a metric of 1000.
RT1 advertised network 202.176.50.0/24 with a metric of 782.
RT3 is directly connected to RT1 using subnet 192.168.1.0.

Correct Answer: RT3 has an IGP metric of 782 to reach 192.168.1.1

You are mixing IGP with IBGP. IGP means routing Interior Gateway Protocols, like IGRP, RIP, EIGRP, OSPF etc.

RT3# show ip route bgp
B  202.176.56.0/24 [200/1782] via 192.168.1.1, 00:18:58

Above route entry is clearly showing that BGP metric is 1782 - which is not included in given answers.
So, "RT3 has a BGP metric of 782 to reach 192.168.1.1." is incorrect. Notice the word "BGP" and "782".

The given answer "RT3 has an IGP metric of 782 to reach 192.168.1.1" can be verified easily from the output of show ip bgp 202.175.56.0

Please pay close attention to terminology and wording traps.

I see what you are saying.  This question is really tricky.  Thank you for the response