Which one of the following, if substituted for the condition that Lewis and Ota do not lecture on the same day as eac...

Victoria on October 15, 2020

Hi @makda.mehari,

Happy to help! This is definitely a tricky question.

Answer choice (C) is incorrect because it is a bit too restrictive.

To start, what is the effect of Rule 3 - i.e. that L and O do not lecture on the same day as each other?

We know that M and N must lecture on the same day. We also know that L and O must lecture on separate days. Therefore, the third spot on the day when M and N lecture must be filled by either L or O.

Ignoring, for the moment, the different times and days, our set-up would look like this:

Day X: M N L/O
Day Y: J K O/L

So, the effect is that J and K must lecture on the same day as each other and L and O are split up over the two days.

Answer choice (A) produces this exact same effect by forcing J and K to lecture on the same day. This leaves us with only one open spot on each day that can be filled by either L or O.

Answer choice (C) is a bit too restrictive because it forces O to lecture on the same day as M and N whereas the original rule makes it possible for O to lecture on the same day as J and K.

The original rule provides us with two options (although we can move the variables around within these options).

Option 1 - O lectures on Thursday

Thursday: J K O
Friday: L M N

Option 2 - O lectures on Friday

Thursday: J K L
Friday: M N O

Answer choice (A) ensures that these two options are still possible.

Answer choice (C) means that M, N, and O must lecture on Friday. Why? Because J, K, and L must lecture on the same day. We know that J lectures at 1. If L lectures on Friday, then they must lecture at 1. Clearly these cannot both be true; therefore, J, K, and L must lecture on Thursday.

Thursday: J K L
1 2 3

Friday: M N O
1 2 3

In this way, answer choice (C) eliminates the possibility of O lecturing on Thursday, meaning that it doesn't have the same effect in determining the schedule for the conference.

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