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!
If I were in this situation in real life, I will ask them about a different place different from the two in the fork, The truth teller will always say "no". On the other hand the liar will say "yes". For that I can identify whether the person is a truth-teller or not, then I will ask him the direct question.
For example, if I am walking in the street and I know one of the branches leads to Ali's house and the other leads to Yasser's house and I seek Ali's house. I would first ask if the right path leads to (some name other than the expected) for example Omar's house which isn't existent. the truth-teller will say "no" while the liar, will say "yes". So I will proceed with the question of interest and determine the result based upon the previous response?
I hope this helps!

If something is wrong or ambiguous, correct me.