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Question

Which of the following statements are not true?

I. A won the bronze medal.

II. E won the silver medal

III. C ended behind A, who ended behind E.

IV. D ended behind B.

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Solution

The correct option is **A** I and II

A couldn't be the 1st or 2nd, for he would be telling the truth: or the 5th, for he would be lying: so he was 3rd or 4th:

If D was telling the truth, then E would be lying Thus D would be the 1st, and lying at the same line which is contradictory. Thus, D is lying, and he is the 1st or 2nd.

If E was lying, D would be the 1st, so E would have to be the 2nd, then D would have been telling the truth. Thus, E is the 3rd, 4th or 5th and D must be 2nd.

Now, only B or C could be the 1st. If B isn't the 1st, as he couldn't be the 2nd, he would have to be the 4th or 5th because C would be the 3rd, But nobody would be the 1st; the only solution then is B, D, E, A and C.

A couldn't be the 1st or 2nd, for he would be telling the truth: or the 5th, for he would be lying: so he was 3rd or 4th:

If D was telling the truth, then E would be lying Thus D would be the 1st, and lying at the same line which is contradictory. Thus, D is lying, and he is the 1st or 2nd.

If E was lying, D would be the 1st, so E would have to be the 2nd, then D would have been telling the truth. Thus, E is the 3rd, 4th or 5th and D must be 2nd.

Now, only B or C could be the 1st. If B isn't the 1st, as he couldn't be the 2nd, he would have to be the 4th or 5th because C would be the 3rd, But nobody would be the 1st; the only solution then is B, D, E, A and C.

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