Read the following details carefully and answer the questions that follow.

Nine consultants are assigned to three different departments: Department Alpha, Department Beta, and Department Gamma. Not less than two consultants and not more than four consultants work in any department. David works only with Emily, but not in department Beta. Frank works in department Beta but not with Ivy. Jack, Karen, and Leo work in the same department. Karen works with Ivy but not in department Alpha. Grace and Henry are two of the consultants.

Jack works in which of the following departments?

Correct Answer: Department Gamma

Step-by-Step Logic and Analysis:

Let us analyze the given information step-by-step to determine which department each consultant works in.

1. Basic Setup & Constraints:

• Total Consultants (9): David, Emily, Frank, Ivy, Jack, Karen, Leo, Grace, Henry.

• Departments (3): Department Alpha, Department Beta, Department Gamma.

• Capacity Constraint: Minimum 2 consultants and Maximum 4 consultants per department.

2. Analyzing David and Emily:

• "David works only with Emily, but not in department Beta."

• "David works only with Emily" means David and Emily are the only two consultants in their department.

• Since David does not work in Department Beta, and their department only has 2 people (satisfying the minimum capacity rule), David and Emily must work together in either Department Alpha or Department Gamma.

3. Analyzing Karen, Ivy, Jack, and Leo:

• "Jack, Karen, and Leo work in the same department."

• "Karen works with Ivy but not in department Alpha."

• Since Karen works with Jack, Leo, and Ivy, all four of them (Jack, Karen, Leo, and Ivy) must be in the same department. This department has a total of 4 consultants (satisfying the maximum capacity rule of 4).

• Since Karen does not work in Department Alpha, the group of 4 (Jack, Karen, Leo, Ivy) cannot be in Department Alpha.

4. Deductive Placement of Groups into Departments:

• We have two key groups identified so far:

1. Group of 2: {David, Emily}

2. Group of 4: {Jack, Karen, Leo, Ivy}

3. Remaining 3 consultants: {Frank, Grace, Henry}

• "Frank works in department Beta but not with Ivy."

• Since Frank is in Department Beta and Ivy is NOT in Department Beta, the group of 4 {Jack, Karen, Leo, Ivy} cannot be in Department Beta either.

• Since the Group of 4 cannot be in Department Alpha or Department Beta, it must be in Department Gamma.

5. Final Distribution:

• Department Gamma (4 consultants): Jack, Karen, Leo, Ivy

• Department Alpha (2 consultants): David, Emily

• Department Beta (3 consultants): Frank, Grace, Henry

Therefore, Jack works in Department Gamma.