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: 
If you ask a liar a question the answer will be lie.

If you ask a liar what his answer will be, he will lie about his answer being a lie and he will say that his answer is the truth.

So if the path leads to ruins and you ask if the path leads to ruins he will lie and say "no". If you ask him if he will answer "yes" he will lie and answer.... "yes".

....

To get the truth out of a liar ask him "What would you say if I asked you..." the liar will lie about lying and give the true answer....[1]

[1](assuming the question was binary yes/no... otherwise he could give a second lie; the lie he \*wouldn't give.)

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Or you could parse it from the top down:

Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "NO"

That's a lie. He would answer yes.

* "Does the right branch leads to the ruins" LIAR: "YES"
* That's a lie. The right branch does not lead to the ruins.
* Conclusion: The left branch lead to the ruins.

Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "NO"

That's the truth. He would answer no.

* "Does the right branch leads to the ruins" TRUTHTELLER : "NO"
* That's the truth. The right branch does not lead to the ruins.
* Conclusion: The left branch lead to the ruins.

Hence "NO" means left branch.

Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" LIAR: "YES"

That's a lie. He would answer no.

* "Does the right branch leads to the ruins" LIAR: "NO"
* That's a lie. The right branch does lead to the ruins.
* Conclusion: The right branch lead to the ruins.

Q: ""if i were to ask you whether the right branch leads to the ruins would you answer yes?"" TRUTHTELLER: "YES"

That's the truth. He would answer yes.

* "Does the right branch leads to the ruins" TRUTHTELLER : "YES"
* That's the truth. The right branch does lead to the ruins.
* Conclusion: The right branch lead to the ruins.

Hence "YES" means right branch.
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!