Question: I get the Extended Euclidean Algorithm but I don't understand what this question is asking me:

In this question we consider arithmetic modulo 60 ("clock arithmetic" on the clock with numbers {0,1,2,3,...,58,59}). 
Which of the following statements apply?

a. 50 X 50 = 40 modulo 60

b. 17 + 50 = 3 modulo 60

c. 4100 x 10 = 0 modulo 60

d. 1/17 = 53 modulo 60

e. 37 + 50 = modulo 60

f. 1/10 is undefined modulo 60

g. 17 - 35 = 42 modulo 60

h. 17 - 25 = 18 modulo 60

I have to pick the right ones but I'm not sure how to work it out? Like if they gave something like 

17x = 1 mod(43) I could solve it but I'm not sure how you would solve the other question

P.S I have the answers I just dont want to look at them as I'd rather try to understand first as this is revision for my exam. thanks

Answer: 
You need to differentiate between two different questions:

Q1: Does the right road lead to the ruins?

Q2: Would you say "yes" to question Q1?

If the right road does lead to the ruins, the liar will say "No" to Q1, and *therefore* say "Yes" to Q2!
You have to consider each of the cases separately. First, let us assume that right path leads to the ruins. Then a villager telling the truth would answer "Yes". A lying villager would answer "Yes" as well, since his answer to the question "Does the right path lead to the ruins?" would be "No".

On the other hand, if the right path leads into the jungle, the answer from the villager telling the truth would be "No". The lying villager would also say "No", because his answer to the question "Does the right path lead to the ruins?" would be "Yes".

Thus, in both cases a "Yes" means that the right path leads to the ruins, and a "No" means that the left path leads to the ruins.