Directions: Study the following information carefully and answer the question given below.
Six professors — U, V, W, X, Y, and Z — deliver guest lectures on six different subjects — Astronomy, Botany, Geology, History, Psychology, and Zoology — on six different days from Monday to Saturday of the same week, but not necessarily in the same order.
Exactly two persons deliver their lectures between the one who lectures on History and X. Not more than two persons deliver their lectures after X. As many persons deliver their lectures before the one who lectures on History as after the one who lectures on Zoology.
V presents immediately after U, but three slots before the one who lectures on Psychology. The one who lectures on Botany presents three slots before Z, but after U. The one who lectures on Astronomy presents immediately before the one who lectures on Botany. Y does not lecture on Botany and delivers their lecture after the one who lectures on Astronomy. W does not lecture on History.
Who among the following lectures on Psychology?
Correct Answer :
Y
Solution :
The correct answer is Y.
Step 1: Determine the positions of X, History, and Zoology.
The six guest lectures take place across six days from Monday (Day 1) to Saturday (Day 6):
1 - Monday, 2 - Tuesday, 3 - Wednesday, 4 - Thursday, 5 - Friday, 6 - Saturday.
We are given:
- Not more than two persons deliver their lectures after X. Thus, X can be scheduled on Day 4, Day 5, or Day 6.
- Exactly two persons deliver their lectures between the one who lectures on History and X.
- As many persons deliver their lectures before History as after Zoology.
If X is placed on Day 4 (Thursday), then History must be on Day 1 (Monday) so that exactly two slots (Day 2 and Day 3) fall between them.
Since zero persons lecture before History on Day 1, zero persons must lecture after Zoology, placing Zoology on Day 6 (Saturday).
Step 2: Place U, V, and Psychology.
We are told that V presents immediately after U, but three slots before the one who lectures on Psychology.
This means:
Slot(V) = Slot(U) + 1
Slot(Psychology) = Slot(V) + 3
Placing U on Day 1 (Monday) means V is on Day 2 (Tuesday), which puts Psychology on Day 5 (Friday) since 2 + 3 = 5.
Step 3: Place Astronomy, Botany, and Z.
We are given:
- Astronomy presents immediately before Botany.
- Botany presents three slots before Z, meaning Slot(Z) = Slot(Botany) + 3.
- Botany presents after U.
Since Day 6 is occupied by Zoology, Z must be the professor delivering the lecture on Day 6 (Zoology).
With Z on Day 6, Botany must be scheduled on Day 3 (Wednesday) since 6 - 3 = 3.
Consequently, Astronomy (immediately before Botany) is scheduled on Day 2 (Tuesday).
Step 4: Assign W and Y to remaining slots.
The remaining available professor slots are Day 3 and Day 5.
- Y delivers their lecture after Astronomy (Day 2) and does not lecture on Botany (Day 3). Therefore, Y must be scheduled on Day 5.
- W does not lecture on History, so W takes the remaining slot on Day 3.
- Geology fill the only remaining subject slot on Day 4 (Thursday) for professor X.
Final Complete Schedule:
- Monday (Day 1): U — History
- Tuesday (Day 2): V — Astronomy
- Wednesday (Day 3): W — Botany
- Thursday (Day 4): X — Geology
- Friday (Day 5): Y — Psychology
- Saturday (Day 6): Z — Zoology
Therefore, professor Y lectures on Psychology.
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