We know that a professor will listen to exactly one speech from each of six students: H, J, K, R, S, and T.
The six speeches will be delivered one at a time, consecutively. Therefore, this is a linear game.
_ _ _ _ _ _ 1 2 3 4 5 6
Now let's go through our conditions.
Rule 1 - the speeches delivered by H, J, and K, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches
Therefore, we cannot have any of the following blocks: |HJK|, |HKJ|, |JKH|, |JHK|, |KJH|, or |KHJ|.
Rule 2 - the speeches delivered by R, S, and T, no matter what their order relative to each other, cannot form a sequence of three consecutive speeches
Therefore, we cannot have any of the following blocks: |RST|, |RTS|, |STR|, |SRT|, |TSR|, or |TRS|.
Rule 3 - H's speech must be earlier than S's speech
H > S
Rule 4 - J's speech can be neither first nor sixth
Rule 5 - T's speech can be neither immediately before nor immediately after J's speech
Therefore, we cannot have either of the following blocks: |JT| or |TJ|.
Now let's address the question stem. We are looking for the answer choice which could represent the order in which the students deliver their speeches.
We can eliminate answer choice (A) because it violates Rule 2. We cannot have an |RST| block.
We can eliminate answer choice (B) because it violates Rule 4. J's speech cannot be sixth.
We can eliminate answer choice (C) because it violates Rule 5. T's speech cannot be immediately after J's speech.
Finally, we can eliminate answer choice (E) because it violates Rule 3. H's speech must be earlier than S's speech.
This means that answer choice (D) should be our correct answer, but let's double check.
R J K T H S 1 2 3 4 5 6
1) The speeches delivered by H, J, and K do not form a sequence of three consecutive speeches. J and K's speeches are given consecutively, but K and H's speeches are separated by T's speech.
2) The speeches delivered by R, S, and T do not form a sequence of three consecutive speeches. R is first, T is fourth, and R is sixth.
3) H's speech is fifth and S's speech is sixth.
4) J's speech is second.
5) J and T's speeches are separated by K's speech
Hope this helps! Please let us know if you have any further questions.
