Five persons A, B, C, D and E (but not necessarily in the same order) have different designations i.e., General Manager (GM), Deputy General Manager (DGM), Assistant Manager (AM), Section Officer (SO), and Clerk in a company. The order of seniority is the same as given above i.e., GM is the senior-most designation and Clerk is the junior-most designation. Each person has different number of pens – 19, 23, 35, 39 and 51 but not necessarily in the same order.

The one who has prime number of pens is not the senior most person but two designations senior to D. C is junior to D. The one who has 39 pens is just senior to E. The difference between the pens of E and C is 4. D has 12 pens more than C. B is junior to the one who has 39 pens.

Which among the following statement(s) is/are true?
I. E has minimum number of pens
II. C is designated as SO
III. D is senior to A

The correct option is Only I.

Step 1: Understand the Designations and Given Data
The designations in order of seniority (from senior-most to junior-most) are:
1. General Manager (GM)
2. Deputy General Manager (DGM)
3. Assistant Manager (AM)
4. Section Officer (SO)
5. Clerk

The available numbers of pens are: 19, 23, 35, 39, and 51.
Among these, the prime numbers are 19 and 23.

Step 2: Determine the Positions of D, C, and the Prime Pen Holder
1. "The one who has a prime number of pens is not the senior-most person but two designations senior to D."
Since GM (position 1) is the senior-most, the person with a prime number of pens cannot be GM.
Two designations senior to D means:
- If D is Clerk (position 5), the prime pen holder would be AM (position 3).
- If D is SO (position 4), the prime pen holder would be DGM (position 2).

2. "C is junior to D."
Since C is junior to D, D cannot be Clerk (position 5) because Clerk is the lowest designation.
Therefore, D must be designated as SO (position 4), which means C must be Clerk (position 5).
Consequently, two designations senior to D (SO) is DGM (position 2), so the person at DGM holds a prime number of pens (19 or 23).

Step 3: Determine the Number of Pens for Each Person
1. "D has 12 pens more than C."
$D-C=12$
Looking at the pen counts (19, 23, 35, 39, 51), the pairs with a difference of 12 are:
- $35-23=12$ (C = 23, D = 35)
- $51-39=12$ (C = 39, D = 51)

2. "The difference between the pens of E and C is 4."
- If C = 23: $23-4=19$, so E = 19 pens (which is in our list).
- If C = 39: $39-4=35$, so E = 35 pens.

Since the person at DGM (position 2) must have a prime number of pens (19 or 23), and C (Clerk) is at position 5 with 23 pens, E (who has 19 pens, also a prime number) must be at DGM (position 2).

Thus, we have:
- C (Clerk) = 23 pens
- E (DGM) = 19 pens
- D (SO) = 35 pens

Step 4: Determine the Positions and Pens for A and B
1. "The one who has 39 pens is just senior to E."
Since E is DGM (position 2), the person just senior to E is GM (position 1). Therefore, the GM has 39 pens.

2. The remaining pen count for position 3 (AM) is 51.

3. "B is junior to the one who has 39 pens."
Since GM has 39 pens, B cannot be GM. Therefore, A must be GM (position 1) and B must be AM (position 3).

Final Arrangement:
- GM (Position 1): A (39 pens)
- DGM (Position 2): E (19 pens)
- AM (Position 3): B (51 pens)
- SO (Position 4): D (35 pens)
- Clerk (Position 5): C (23 pens)

Step 5: Evaluate the Given Statements
- Statement I: E has minimum number of pens — True (E has 19 pens, which is the smallest value).
- Statement II: C is designated as SO — False (C is designated as Clerk).
- Statement III: D is senior to A — False (D is SO, whereas A is GM, so D is junior to A).

Hence, only statement I is true.