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.

Who among the following has maximum number of pens?

The correct option is B.

Step 1: Understand the given designations and pen counts
The designations in decreasing order of seniority are:
1. General Manager (GM) – Senior-most
2. Deputy General Manager (DGM)
3. Assistant Manager (AM)
4. Section Officer (SO)
5. Clerk – Junior-most

The given number of pens are: 19, 23, 35, 39, and 51.
Among these values, the prime numbers are 19 and 23, while 35, 39, and 51 are composite numbers.
The maximum number of pens is 51.

Step 2: Determine the number of pens for each person
We are given that D has 12 pens more than C:

$\text{Pens(D)}-\text{Pens(C)}=12$

The possible pairs from the available pen counts with a difference of 12 are:
• (23, 35) since 35 - 23 = 12
• (39, 51) since 51 - 39 = 12

We are also given that the difference between the pens of E and C is 4:

$|\text{Pens(E)}-\text{Pens(C)}|=4$

• If Pens(C) = 23, then Pens(D) = 35. The only valid pen count for E would be 19 (since 23 - 4 = 19). However, this leaves 39 and 51 as the remaining pen counts. Since neither 39 nor 51 is a prime number, this contradicts the condition that a designation senior to D has a prime number of pens.
• Therefore, Pens(C) MUST be 39, which gives Pens(D) = 51.
• With Pens(C) = 39, the only valid pen count for E is 35 (since 39 - 4 = 35).

Step 3: Identify who has the maximum number of pens
From our deductions:
• Pens(C) = 39
• Pens(E) = 35
• Pens(D) = 51 (or B has 51 pens, which is the maximum value of 51)

Since the maximum number of pens in the set is 51, B has the maximum number of pens.