Directions: Read the following information carefully and answer the question that follows.

Eight members — K, T, U, V, W, X, Y, and Z — hold eight distinct academic designations in a university: Chancellor, Vice-Chancellor, Dean, Department Head, Senior Professor, Associate Professor, Assistant Professor, and Lecturer. The order of seniority is from Chancellor (the senior-most) down to Lecturer (the junior-most).

K is the Lecturer of the university.
Three persons hold designations between K and T.
X holds a designation senior to Dean, but X is not the Vice-Chancellor.
The number of persons senior to V is equal to the number of persons junior to W.
Two persons hold designations between V and U.
Z is senior to Y, but junior to Vice-Chancellor.

How many members hold a designation junior to Z?

The correct answer is Five.

Step-by-Step Explanation:

We are given eight academic designations in order of seniority from highest to lowest:
1. Chancellor (Senior-most)
2. Vice-Chancellor
3. Dean
4. Department Head
5. Senior Professor
6. Associate Professor
7. Assistant Professor
8. Lecturer (Junior-most)

Let us determine the positions of the eight members (K, T, U, V, W, X, Y, Z) step-by-step based on the given clues:

Step 1: Position of K and T
• K is the Lecturer of the university. Therefore, K = Lecturer (Position 8).
• Three persons hold designations between K and T. Moving 3 positions up from Lecturer (Position 8), we get T = Department Head (Position 4).

Step 2: Position of X
• X holds a designation senior to Dean (Position 3), but X is not the Vice-Chancellor (Position 2).
• Therefore, X = Chancellor (Position 1).

Step 3: Positions of V, W, and U
• The number of persons senior to V is equal to the number of persons junior to W.
• The remaining available positions are 2, 3, 5, 6, and 7.
• The symmetrical pairs of positions that satisfy this condition are (2, 7) and (3, 6).
• We are also given that two persons hold designations between V and U.
• If V were at Position 3 or 6, placing U two positions away would conflict with W. Thus, V must be at Position 2 and W at Position 7.
• So, V = Vice-Chancellor (Position 2) and W = Assistant Professor (Position 7).
• Placing U two positions junior to V (Position 2) gives U = Senior Professor (Position 5).

Step 4: Positions of Z and Y
• The remaining vacant positions are 3 and 6.
• Z is senior to Y, so Z = Dean (Position 3) and Y = Associate Professor (Position 6).

Final Academic Seniority Order:
1. Chancellor: X
2. Vice-Chancellor: V
3. Dean: Z
4. Department Head: T
5. Senior Professor: U
6. Associate Professor: Y
7. Assistant Professor: W
8. Lecturer: K

Conclusion:
Z holds the designation of Dean (Position 3).
The members holding a designation junior to Z are T, U, Y, W, and K, which equals 5 members in total.