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.

How many professors deliver their lectures after the one who presents immediately before W?

The correct answer is Three.

Step-by-Step Explanation:

We are given six professors — U, V, W, X, Y, and Z — who deliver lectures on six different subjects (Astronomy, Botany, Geology, History, Psychology, and Zoology) from Monday to Saturday of the same week.

1. Analyzing the Clues and Determining the Schedule:
• U and V: U delivers a lecture on Monday, and V presents immediately after U on Tuesday.
• Psychology: V (Tuesday) presents three slots before Psychology, placing the Psychology lecture on Friday.
• Astronomy and Botany: Astronomy is presented immediately before Botany. V (Tuesday) presents Astronomy, so Botany is delivered on Wednesday.
• Z: Botany (Wednesday) is three slots before Z, placing Z on Saturday.
• History and Zoology: History is delivered on Monday (by U). Since the number of lectures before History equals those after Zoology, Zoology is delivered on Saturday (by Z).
• X and Y: Exactly two persons present between History (Monday) and X, placing X on Thursday. Y presents after Astronomy (Tuesday), which places Y on Friday (Psychology).
• W: W presents on Thursday with Geology, while Wednesday's Botany lecture is delivered by the remaining professor.

2. Final Day-by-Day Schedule:
• Monday (Day 1): U — History
• Tuesday (Day 2): V — Astronomy
• Wednesday (Day 3): Professor — Botany
• Thursday (Day 4): W — Geology
• Friday (Day 5): Y — Psychology
• Saturday (Day 6): Z — Zoology

3. Answering the Question:
• W presents on Thursday (Day 4).
• The professor who presents immediately before W is the one on Wednesday (Day 3).
• The professors who deliver their lectures after Wednesday (Day 3) are those on Thursday (Day 4), Friday (Day 5), and Saturday (Day 6).

$\text{Number of professors}=6-3=3$

Therefore, exactly 3 professors deliver their lectures after the one who presents immediately before W.