# Which one of the following must be a day on which Doctor Yamata lectures?

Charlotte on August 20, 2019

Question

Hi, can someone please assist me with this question?

Replies

Irina on August 20, 2019

Let's look at the setup for this game. Doctor Y works only on M, T, W, F and . She performs 4 different activities - lecturing (L), operating (O), treating patients (T), and research (R). Each day she performs one activity in the morning and one in the afternoon.

am ___ ___ ___ ___ ___
pm ___ ___ ___ ___ ___
M T W F S

Let's look at the rules:

(1) She performs operations on exactly three mornings.

OOO AM

(2) If she operates on Monday, she does not operate on Tuesday.

O (m) -> ~ O(t)

This rule tells us that she could either operate on Monday or Tuesday, or neither, but not both.

(3) She lectures in the afternoon on exactly two consecutive calendar days.

LL PM consecutive

This rule is important because the days she works are not consecutive as she skips over Thursday.

(4) She treats patients on exactly one morning and exactly 3 afternoons

T AM
TTT PM

(5) She conducts research on exactly one morning

R AM

(6) On Saturday, she neither lectures nor performs operations.

S -> ~L & ~ O

am ___ ___ ___ ___ ___
pm ___ ___ ___ ___ ___
M T W F S
~L
~O

Notice that there are ten time slots and the rules tell us the exact number of times each activity is performed adding up to ten and whether each activity is performed in the morning or the afternoon. Putting the rules together we know that:

-in the mornings Y does exactly 3 O, 1 T, and 1 R
-in the afternoon Y does exactly 2 L and 3 T.

am ___ ___ ___ ___ ___ 3 - O, 1 -T, 1 - R
pm ___ ___ ___ ___ ___ 2- L, 3 - T
M T W F S
~L
~O

We can also infer that since she must operate 3 days of the week but cannot operate S per rule (6) and can only operate either on M or T but not both per rule (2), she must operate on W & F as well as either M or T.

/o /o /t /r
am ___ ___ o o ___ 3 - O, 1 -T, 1 - R
pm ___ ___ ___ ___ t 2- L, 3 - T
M T W F S
~L
~O

We can also conclude that S morning must be either T or R per rule (6), and S afternoon must be T since the only activities in the afternoon are either L or T, and L cannot go on S at all per rule (6).

We can further infer that since she lectures on exactly two consecutive afternoons per rule(3) and cannot lecture on S per rule (6), she cannot lecture on F as well and must lecture either on MT or TW, or in other words, she must lecture on T and either on M or W.

And lastly, since the only afternoon activities are L or T, and L cannot go on F, she must teach on F afternoon as well.

Let's put all the inferences on our diagram:

/o /o /t /r
am ___ ___ o o ___ 3 - O, 1 -T, 1 - R

/L/T /T/L
pm ___ L ___ T T 2- L, 3 - T
M T W F S

Now the question asks us which one of the following must be a day on which Doctor Yamata lectures?

We can tell by looking at our initial setup that she must lecture on Tuesday, answer choice (B).

Does this make sense?

Let me know if you have any further questions.

on September 8, 2020

And lastly, since the only afternoon activities are L or T, and L cannot go on F, she must teach on F afternoon as well.

Why do you say the doctor can't lecture on Friday? The rule states that the doctor neither lectures or operates on Saturday. Is this an error in setting up the game or am I missing something?