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A puzzle closer to Gmat logic. I think I encountered a [#permalink]
16 Mar 2004, 20:41

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A puzzle closer to Gmat logic. I think I encountered a similar one of the gmat800 tests(?).

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Two men stand at a fork in the road. One fork leads to place X; the other fork leads to place Y. One of these people always answers the truth to any yes/no question which is asked of him. The other always lies when asked any yes/no question. By asking one yes/no question, can you determine the road to X?

Ask any of them this question:
What will the other say if I asked him whether the left fork leads to place X?
If you talked to the one who always lies:
If he says that the one who tells the truth will say yes, then you would know that it's not true because he lies. Thus, left fork will NOT lead to place X.
If you talked to the one who always says the truth:
If he says that the one who tells a lie will say yes, then it MUST be true that the other person must tell a lie and left fork will then NOT lead to place X.
Thus, in above instances, when BOTH say yes, you would take other route! It logically follows that when both say no, you would take the left fork as the one going to place X _________________

If I ask you whether the left road leads to place X, will you answer, yes?

In any case you"ll get the right direction.

If the one who lies says yes, then you would know that answer is no.
If the one who says the truth says yes, then you would know answer is yes. Now, in this instance, both of them said yes but outcome is different. Since you don't know which one you talked to, how would you know if it's the one, the one who lies or who says the truth, whom you talked to? Since outcomes are different, you cannot ask your question. _________________

If I ask you whether the left road leads to place X, will you answer, yes?

In any case you"ll get the right direction.

If the one who lies says yes, then you would know that answer is no. If the one who says the truth says yes, then you would know answer is yes. Now, in this instance, both of them said yes but outcome is different. Since you don't know which one you talked to, how would you know if it's the one, the one who lies or who says the truth, whom you talked to? Since outcomes are different, you cannot ask your question.

Actually I agree with Agent_777's qs.
Assume the road to left is indeed leads to X. Now if you ask the person who lies, the qs whether the left road leads to X, he has to answer 'No'. But the question is whether he will answer yes to this question. Again as he has to lie, he has to say 'yes'.
Ask the question to a person who tells the truth, he also will answer yes. Thus doesnt matter whom you ask, the answer will tell you whether the road to left leads to X.

Thus if the answer is yes, the road to left leads to X, if the answer is no, the road to right leads to X.

If I ask you whether the left road leads to place X, will you answer, yes?

In any case you"ll get the right direction.

If the one who lies says yes, then you would know that answer is no. If the one who says the truth says yes, then you would know answer is yes. Now, in this instance, both of them said yes but outcome is different. Since you don't know which one you talked to, how would you know if it's the one, the one who lies or who says the truth, whom you talked to? Since outcomes are different, you cannot ask your question.

Actually I agree with Agent_777's qs. Assume the road to left is indeed leads to X. Now if you ask the person who lies, the qs whether the left road leads to X, he has to answer 'No'. But the question is whether he will answer yes to this question. Again as he has to lie, he has to say 'yes'. Ask the question to a person who tells the truth, he also will answer yes. Thus doesnt matter whom you ask, the answer will tell you whether the road to left leads to X.

Thus if the answer is yes, the road to left leads to X, if the answer is no, the road to right leads to X.

Nice, I overlooked that solution. However, did you check my solution as well? I stand my ground that my solution will always give you the right answer as well. Test it. _________________