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?
Correct Answer :
Grace
Solution :
The correct option is Grace.
Let us analyze the given conditions step-by-step to determine the department assignment for each consultant:
1. Total Consultants: There are 9 consultants: David, Emily, Frank, Ivy, Jack, Karen, Leo, Grace, and Henry.
2. Departments: Department Alpha, Department Beta, and Department Gamma.
3. Capacity Constraint: Each department has at least 2 and at most 4 consultants (2 ≤ capacity ≤ 4).
Now let's trace the statements:
- "Jack, Karen, and Leo work in the same department." This group consists of 3 consultants.
- "Karen works with Ivy but not in department Alpha." This means Ivy works in the same department as Karen. Therefore, Jack, Karen, Leo, and Ivy all work together in the same department. Since a department can hold a maximum of 4 consultants, this department is now full with 4 members: {Jack, Karen, Leo, Ivy}.
- Since Karen does not work in Department Alpha, and Frank works in Department Beta but not with Ivy, Ivy (and her group of 4) cannot be in Department Beta either. Thus, {Jack, Karen, Leo, Ivy} must be assigned to Department Gamma.
- "David works only with Emily, but not in department Beta." Since David works only with Emily, their department contains exactly 2 consultants: {David, Emily}. Since David does not work in Department Beta, and Department Gamma is already full, David and Emily must work in Department Alpha.
- "Frank works in department Beta." We know Frank is in Department Beta. So far, Department Alpha has 2 consultants {David, Emily}, Department Gamma has 4 consultants {Jack, Karen, Leo, Ivy}, making a total of 6 consultants. The remaining 3 consultants—Frank, Grace, and Henry—must work in Department Beta.
To summarize the department assignments:
- Department Alpha (2): David, Emily
- Department Beta (3): Frank, Grace, Henry
- Department Gamma (4): Jack, Karen, Leo, Ivy
Therefore, among the options provided, Grace works in Department Beta.
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