Directions: Study the following information carefully and answer the question given below.
Eight professionals — A, B, C, D, E, F, G, and H — work in an organization at different designations, namely Director, Vice President (VP), General Manager (GM), Senior Manager (SM), Manager, Assistant Manager (AM), Executive, and Trainee, but not necessarily in the same order. The designations are given in decreasing order of seniority such that Director is the senior-most post and Trainee is the junior-most post.
F is three ranks junior to C. The number of persons senior to H is equal to the number of persons junior to B. Only two persons are designated between H and F. D is two ranks senior to G. A is senior to E but junior to D.
How many persons are designated between D and the person who is immediately senior to H?
Correct Answer :
Two
Solution :
The correct option is Two.
Step 1: Understand the designation hierarchy.
The eight designations in decreasing order of seniority (from 1 to 8) are:
1. Director (Senior-most)
2. Vice President (VP)
3. General Manager (GM)
4. Senior Manager (SM)
5. Manager
6. Assistant Manager (AM)
7. Executive
8. Trainee (Junior-most)
Step 2: Determine the relative positions of C, F, and H.
- F is three ranks junior to C, which means Rank(F) = Rank(C) + 3.
- Two persons are designated between H and F. This means Rank(H) = Rank(F) + 3 or Rank(H) = Rank(F) - 3.
- If Rank(H) = Rank(F) - 3, then Rank(H) would equal Rank(C), which is impossible since they are distinct persons. Therefore, Rank(H) = Rank(F) + 3 = Rank(C) + 6.
- Since the lowest rank is 8, Rank(C) can only be 1 or 2.
Case 1: Rank(C) = 1 (Director)
- Rank(F) = 1 + 3 = 4 (SM)
- Rank(H) = 4 + 3 = 7 (Executive)
- Since 6 persons are senior to H (Rank 7), exactly 6 persons must be junior to B. This places B at Rank 2 (VP).
Case 2: Rank(C) = 2 (VP)
- Rank(F) = 2 + 3 = 5 (Manager)
- Rank(H) = 5 + 3 = 8 (Trainee)
- Since 7 persons are senior to H, B must be at Rank 1 (Director).
- D is two ranks senior to G (Rank(G) - Rank(D) = 2), forcing D = 4 and G = 6. The remaining vacant positions for A and E would be 3 and 7. However, A is senior to E but junior to D (Rank(D) < Rank(A) < Rank(E)), which cannot be satisfied because rank 7 is junior to rank 3. Thus, Case 2 is invalid.
Step 3: Complete the arrangement using Case 1.
- Positions filled so far: C = 1, B = 2, F = 4, H = 7.
- D is two ranks senior to G (Rank(G) - Rank(D) = 2). The available vacant positions with a difference of 2 are Rank 3 and Rank 5. Hence, D = 3 (GM) and G = 5 (Manager).
- The remaining vacant positions are Rank 6 and Rank 8 for A and E.
- Since A is senior to E but junior to D, A = 6 (AM) and E = 8 (Trainee).
Final Designation Schedule:
1. Director: C
2. Vice President (VP): B
3. General Manager (GM): D
4. Senior Manager (SM): F
5. Manager: G
6. Assistant Manager (AM): A
7. Executive: H
8. Trainee: E
Step 4: Evaluate the question.
- The person immediately senior to H (Executive, Rank 7) is A (Assistant Manager, Rank 6).
- D is General Manager (Rank 3).
- The persons designated between D (Rank 3) and A (Rank 6) are F (Rank 4) and G (Rank 5).
Therefore, exactly Two persons are designated between D and the person immediately senior to H.
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