Who among the following is designated as GM? Study the following information carefully and answer the questions given below:

Nine persons - P, Q, R, S, T, U, V, W and X are working in the company at different designations such as MD, CEO, CFO, CRO, COO, GM, DM, HR and TL but not necessarily in the same order. The designations are given in decreasing order, such that MD is the senior-most designation and TL is the junior-most designation.

X is four persons junior to Q who is senior to CRO. The number of persons senior to Q is one less than the number of persons junior to S. Only three persons are designated between S and T. P is two persons junior to T. The number of persons designated between P and U is one less than the number of persons designated between U and V who is senior to X. W is senior to R who is not TL.

To find who is designated as GM, we can analyze the clues and construct the step-by-step arrangement of the nine employees based on their designations.

First, let's list the designations in decreasing order of seniority (from 1 as senior-most to 9 as junior-most):

1. MD
2. CEO
3. CFO
4. CRO
5. COO
6. GM
7. DM
8. HR
9. TL

Now, let's analyze the given clues step-by-step:

Step 1: Positions of Q, X, S, T, and P
1. "Q is senior to CRO": This means Q must hold one of the top three designations (MD, CEO, or CFO), i.e., Rank(Q) < 4.
2. "X is four persons junior to Q": This means $\mathrm{Rank}\left(X\right)=\mathrm{Rank}\left(Q\right)+4$.
3. "The number of persons senior to Q is one less than the number of persons junior to S":
The number of persons senior to Q is $\mathrm{Rank}\left(Q\right)-1$.
The number of persons junior to S is $9-\mathrm{Rank}\left(S\right)$.
Thus, $\mathrm{Rank}\left(Q\right)-1=9-\mathrm{Rank}\left(S\right)-1\Rightarrow \mathrm{Rank}\left(Q\right)+\mathrm{Rank}\left(S\right)=9$.
4. "Only three persons are designated between S and T": This means $\left|\mathrm{Rank}\right(S)-\mathrm{Rank}(T\left)\right|=4$.
5. "P is two persons junior to T": This means $\mathrm{Rank}\left(P\right)=\mathrm{Rank}\left(T\right)+2$.

Let's evaluate the cases based on the possible ranks for Q:

• If Q is CEO (Rank 2):
  - X must be GM (Rank $2+4=6$).
  - S must be DM (Rank $9-2=7$).
  - Since $|7-\mathrm{Rank}(T\left)\right|=4$, T must be CFO (Rank 3).
  - P must be COO (Rank $3+2=5$).

Step 2: Positions of V, U, W, and R
1. "V is senior to X": Since X is Rank 6, V must have a rank less than 6. The remaining vacant ranks are 1, 4, 8, and 9.
2. "The number of persons designated between P and U is one less than the number of persons designated between U and V":
Let's test V = CRO (Rank 4) and U = TL (Rank 9):
- Persons between P (5) and U (9) = 3 (Ranks 6, 7, 8).
- Persons between U (9) and V (4) = 4 (Ranks 5, 6, 7, 8).
Since 3 is one less than 4, this holds true! Thus, V is CRO (Rank 4) and U is TL (Rank 9).
3. "W is senior to R who is not TL": The remaining vacant ranks are MD (Rank 1) and HR (Rank 8). Since W is senior to R, W must be MD (Rank 1) and R must be HR (Rank 8). R is indeed not TL.

Final Arrangement:

Therefore, X is designated as the GM.