Six students P, Q, R, S, T, and U are the top six rankers in a class. Each student has a unique rank from 1 to 6, where rank 1 is the highest and rank 6 is the lowest. Who got the 6th rank?

I. Q scored less than both R and U. P scored more than T but less than S.

II. Q got the second lowest rank and U got the second highest rank. R scored less than P.

Question

Six students P, Q, R, S, T, and U are the top six rankers in a class. Each student has a unique rank from 1 to 6, where rank 1 is the highest and rank 6 is the lowest. Who got the 6th rank?

I. Q scored less than both R and U. P scored more than T but less than S.

II. Q got the second lowest rank and U got the second highest rank. R scored less than P.

Accepted Answer

**Solution:**

1. From statement I:
   - Q scored less than R and U.
   - P scored more than T but less than S.

This gives some relative positions but does not clearly identify who is ranked 6th.

2. From statement II:
   - Q is ranked second lowest (rank 5).
   - U is ranked second highest (rank 2).
   - R scored less than P.

This provides more specific rank information but still does not pinpoint the 6th rank.

3. Combining both statements:
   - Since Q is second lowest (rank 5), the only rank lower than Q is 6th.
   - Q scored less than R and U, so R and U are ranked higher than Q.
   - U is second highest (rank 2), so ranks 1 and 2 are taken by S and U (since P is less than S and more than T, and S is higher than P).
   - P is between S and T.
   - R scored less than P, so R is ranked lower than P.

Putting all together, the only student left for rank 6 is T.

**Answer:** Both statements I and II together are sufficient to determine that T got the 6th rank.

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