Question Details

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.

Who among the following works in department Beta?

Options

A

Grace

B

Jack

C

David

D

Both Jack and David

E

Both Grace and David

Show Answer

Correct Answer :

Option A

Grace

Solution :

The correct answer is Grace.

Let's analyze the given details step-by-step to determine the department assignment for each consultant.

1. Basic Constraints:
- Total consultants = 9 (David, Emily, Frank, Ivy, Jack, Karen, Leo, Grace, Henry).
- Total departments = 3 (Department Alpha, Department Beta, Department Gamma).
- Each department has between 2 and 4 consultants.

2. Analyzing Consultant Groups & Departments:
- David and Emily: "David works only with Emily, but not in department Beta."
This means David and Emily are the only two consultants in their department. Since David does not work in Beta, this 2-person department must be either Alpha or Gamma.
- Jack, Karen, and Leo: "Jack, Karen, and Leo work in the same department."
So, {Jack, Karen, Leo} form a group of 3 people in one department.
- Karen and Ivy: "Karen works with Ivy but not in department Alpha."
Since Karen works with Ivy, Ivy must also be in the same department as Jack, Karen, and Leo. Thus, the group becomes {Jack, Karen, Leo, Ivy}, which has 4 consultants.
Since Karen does not work in Alpha, this 4-person group {Jack, Karen, Leo, Ivy} cannot be in Alpha.

3. Determining Department Assignments:
We have three groups of consultants to place into three departments:
- A 2-consultant group: {David, Emily}
- A 4-consultant group: {Jack, Karen, Leo, Ivy}
- The remaining consultants: Frank, Grace, and Henry (3 consultants).

Let's assign them to the departments:
- "Frank works in department Beta but not with Ivy."
Since Frank is in Beta, and Ivy is in the 4-consultant group {Jack, Karen, Leo, Ivy}, the 4-person group CANNOT be in Beta. Also, as established earlier, this 4-person group cannot be in Alpha. Therefore, {Jack, Karen, Leo, Ivy} must be in Department Gamma.
- Now, David and Emily work only together in a 2-person department. Since Gamma has 4 people and Beta has Frank (plus others), {David, Emily} must be in Department Alpha.
- Consequently, the remaining consultants—Frank, Grace, and Henry—must be in Department Beta.

Summary of Departments:
- Department Alpha (2 people): David, Emily
- Department Beta (3 people): Frank, Grace, Henry
- Department Gamma (4 people): Jack, Karen, Leo, Ivy

Therefore, among the options provided, Grace works in Department Beta.

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