Study the following information carefully and answer the question given below

Eight persons from A to H has different degree i.e., BBA, MBA and MCA but not necessarily in the same order. At least two but not more than three persons have the same degree. Consecutive alphabetically named persons do not have the same degree.

D does not have an MBA degree. Only C and F have the same degree but not a BBA degree. Both A and H have the same degree but not as D have. E does not have an MBA degree. B does not have a BBA degree.

Who among the following has an MCA degree?

Correct Option: G

Let's analyze the given puzzle step-by-step to determine the degree of each of the eight persons (A, B, C, D, E, F, G, H):

Given Rules and Conditions:

1. Degrees available: BBA, MBA, and MCA.

2. Total persons = 8. At least 2 and at most 3 persons have the same degree.

3. Consecutive alphabetically named persons do not have the same degree (e.g., A and B cannot have the same degree, B and C cannot, etc.).

Step-by-step Deduction:

1. Identify the degree of C and F:

"Only C and F have the same degree but not a BBA degree."

This means exactly two persons have this specific degree, and those two are C and F. Since it is not BBA, it must be either MBA or MCA.

Since C and F are the only ones with this degree, the count for this degree is 2.

The remaining 6 persons must be distributed among the other two degrees. Since maximum 3 persons can have any degree, the distribution of persons per degree across all 8 people must be 3, 3, 2.

2. Determine D and E's degrees:

"D does not have an MBA degree."

"E does not have an MBA degree."

Also, D and E cannot be C and F (since C and F are the only two with their degree). Thus, D and E must be in one of the other degrees.

3. Analyze A and H:

"Both A and H have the same degree but not as D have."

Since A and H have a degree different from D, D has a degree with multiple people (not the exclusive C/F degree).

If D does not have MBA, D must have BBA or MCA.

Let's test the possibilities for the exclusive degree of {C, F}:

Suppose {C, F} have MCA (count = 2).

Then MBA must have 3 persons, and BBA must have 3 persons.

D does not have MBA, so D must have BBA.

Since A and H have a degree different from D, A and H must have MBA (as MCA is full with C and F).

E does not have MBA, so E must have BBA.

Now B: B cannot have BBA (given: "B does not have a BBA degree"). B also cannot have MCA (since only C and F have MCA). Therefore, B must have MBA.

So MBA currently has: A, H, B (3 persons - full!).

BBA currently has: D, E. We need 1 more person for BBA, which must be G.

Let's check consecutive alphabet constraints for this case:

- BBA: D, E, G

- MBA: A, B, H

- MCA: C, F

Check consecutive alphabets:

- A and B both have MBA → Violates rule: Consecutive alphabetically named persons (A and B) cannot have the same degree!

Therefore, {C, F} cannot have MCA. {C, F} must have MBA!

4. Placing everyone with {C, F} = MBA (count = 2):

Since MBA has C and F (and no one else), the remaining degrees BBA and MCA must have 3 persons each.

- D does not have MBA. So D is either BBA or MCA.

- E does not have MBA. So E is either BBA or MCA.

- B does not have BBA, and MBA is full (only C and F). Therefore, B must have MCA.

Now consider C and D: D cannot be adjacent to C if they share a degree, but here C is MBA. D is either BBA or MCA.

Since B has MCA, and consecutive alphabetically named persons cannot have the same degree:

- A cannot have MCA (since B has MCA). So A must have BBA.

- C cannot have MCA (C is MBA).

Since A and H have the same degree, H must also have BBA.

Since "A and H have the same degree but not as D have":

A and H have BBA, so D must have MCA.

Let's check the persons placed so far:

- MBA (2 persons): C, F

- BBA (3 persons): A, H, ...

- MCA (3 persons): B, D, ...

Remaining persons to place: E and G.

We know D has MCA. Since D and E are consecutive alphabets, E cannot have MCA (since D has MCA).

Therefore, E must have BBA.

Now BBA has 3 persons: A, H, E (BBA is now full!).

The remaining person, G, must have MCA.

Final Degree Distribution:

- MBA: C, F

- BBA: A, E, H

- MCA: B, D, G

Let's double-check all conditions:

1. Total counts: MBA (2), BBA (3), MCA (3) - Valid!

2. Consecutive alphabet check:

- A (BBA), B (MCA) - Different

- B (MCA), C (MBA) - Different

- C (MBA), D (MCA) - Different

- D (MCA), E (BBA) - Different

- E (BBA), F (MBA) - Different

- F (MBA), G (MCA) - Different

- G (MCA), H (BBA) - Different

All consecutive pairs have different degrees!

Thus, the persons who have an MCA degree are B, D, and G.

Among the given options, G is listed as having an MCA degree.