Twenty-one employees hold different designations in a bank: CEO, MD, DGM, AGM, Manager, and Clerk. The hierarchy from senior-most to junior-most is CEO MD DGM AGM Manager Clerk. The number of employees at each designation is exactly one more than the number at the immediately senior designation. For example, if there are 3 AGMs, then there are 4 Managers, and so on.

Given:
- P, T, and W share the same designation.
- S is senior to W.
- X is senior to U, who is not an AGM.
- R and V share the same designation.
- Neither B nor H is a Manager, but both share the same designation.
- D, E, and H share the same designation, which is junior to Q and T.
- Q is junior to U.
- The number of persons senior to Q and T is the same.
- X is junior to N but senior to R.
- A, L, and M share the same designation.
- W is not a Manager.
- R is neither Manager nor Clerk.
- Z and Y are senior to G and O.

These employees are transferred to three departments: HR, Marketing, and Legal, based on the following rules:

I. No transfers for the top two designations; they become leaders of HR, Marketing, and Legal respectively in alphabetical order.

II. Employees whose names start with a consonant before 'M' in the alphabet go to HR.

III. Employees whose names start with a consonant after 'M' go to Marketing.

IV. The rest go to Legal.

**Question:** How many employees are transferred to the Legal department?

Question

Twenty-one employees hold different designations in a bank: CEO, MD, DGM, AGM, Manager, and Clerk. The hierarchy from senior-most to junior-most is CEO > MD > DGM > AGM > Manager > Clerk. The number of employees at each designation is exactly one more than the number at the immediately senior designation. For example, if there are 3 AGMs, then there are 4 Managers, and so on.

Given:
- P, T, and W share the same designation.
- S is senior to W.
- X is senior to U, who is not an AGM.
- R and V share the same designation.
- Neither B nor H is a Manager, but both share the same designation.
- D, E, and H share the same designation, which is junior to Q and T.
- Q is junior to U.
- The number of persons senior to Q and T is the same.
- X is junior to N but senior to R.
- A, L, and M share the same designation.
- W is not a Manager.
- R is neither Manager nor Clerk.
- Z and Y are senior to G and O.

These employees are transferred to three departments: HR, Marketing, and Legal, based on the following rules:

I. No transfers for the top two designations; they become leaders of HR, Marketing, and Legal respectively in alphabetical order.

II. Employees whose names start with a consonant before 'M' in the alphabet go to HR.

III. Employees whose names start with a consonant after 'M' go to Marketing.

IV. The rest go to Legal.

**Question:** How many employees are transferred to the Legal department?

Accepted Answer

**Solution:**

1. **Determine the number of persons at each designation:**
   - Since the number at each designation is one more than the immediate senior designation and total persons are 21, let the number of CEOs be *x*.
   - Then MD = *x + 1*, DGM = *x + 2*, AGM = *x + 3*, Manager = *x + 4*, Clerk = *x + 5*.
   - Sum: $x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 21$.
   - Simplify: $6x + 15 = 21 ightarrow 6x = 6 ightarrow x = 1$.

2. **Assign numbers:**
   - CEO = 1
   - MD = 2
   - DGM = 3
   - AGM = 4
   - Manager = 5
   - Clerk = 6

3. **Assign persons to designations (from given clues):**
   - CEO: N
   - MD: S, X
   - DGM: U, R, V
   - AGM: P, T, Q, W
   - Manager: A, L, M, Z, Y
   - Clerk: B, D, G, H, E, O

4. **Department leaders (top two posts no transfer):**
   - CEO (N) leads HR
   - MD (S, X) leads Marketing and Legal respectively in alphabetical order: S leads Marketing, X leads Legal

5. **Transfer rules:**
   - Names starting with consonants before 'M' go to HR.
   - Names starting with consonants after 'M' go to Marketing.
   - The rest go to Legal.

6. **Classify employees by first letter:**
   - HR: L, B, D, G, H (consonants before M)
   - Marketing: R, V, P, Q, T, W, Y, Z (consonants after M)
   - Legal: U, A, E, O, M (others - vowels and A, E, O, U, M)

7. **Count Legal department employees:**
   - U, A, E, O, M → 5 persons

**Answer:** Five

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