# Which one of the following CANNOT be true of the week's tour schedule?

Ben-Couse on September 30, 2020

GAME SETUP

What is the game setup for this game?

Victoria on October 3, 2020

Hi @Ben-Couse,

Happy to help!

We know that a company will tour its three divisions: O, P, and S.

The tours will be conducted from Monday to Friday. One tour will be conducted each day for a total of five tours.

_ _ _ _ _
M T W R F

Now let's go through our conditions.

Rule 1 - each division is toured at least once

Rule 2 - O is not toured on M

Therefore, either P or S is toured on M.

Rule 3 - P is not toured on W

Therefore, either O or S is toured on W.

Rule 4 - S is toured on two consecutive days and on no other days

This means that either O or P is also toured twice for a total of five tours.

Rule 5 - if O is toured on R, then P is toured on F

OR --> PF
Not PF --> Not OR

So, what do we know so far?

P/S _ O/S _ _
M T W R F

This gives us a few different possibilities.

If S is toured on M, then it must also be toured on T and O is toured on W.

Option 1:

S S O P/O O/P
M T W R F

If S is toured on W, then it must also be toured on either T or R and P is toured on M.

Option 2:

P S S O/P P/O
M T W R F

Option 3:

P O/P S S P/O
M T W R F

Now let's address the question stem. We are looking for the answer choice that cannot be true of the week's tour schedule. Therefore, the incorrect answer choices could be true.

We can eliminate answer choice (A) because Option 1 above tells us this could be true. If S is toured on M, then S must also be toured on T.

We can eliminate answer choice (B) because it is possible in both Options 2 and 3.

Option 2:

P S S O P
M T W R F

Option 3:

P O S S P
M T W R F

We can eliminate answer choice (D) because Option 1 tells us that this could be true.

Option 1:

S S O P O
M T W R F

We can also eliminate answer choice (E) because Option 1 tells us that this could be true.

Option 1:

S S O P P
M T W R F

Therefore, this means that answer choice (C) should be our correct answer, but let's double check.

We know that S cannot be toured on T and R because S is toured on two consecutive days.

Neither O nor P could be toured on both T and R because there would be no two remaining consecutive tour slots for tours of S.

_ O/P _ P/O _
M T W R F

Hope this helps! Please let us know if you have any further questions.