Here’s a structured analysis and solution for a 2018 CAT DILR (Data Interpretation and Logical Reasoning) Slot 1 question, assuming a typical game-based arrangement problem (common in CAT DILR). Since I don’t have the exact 2018 question, I’ll create a hypothetical example based on recurring patterns in CAT DILR:
Problem Statement (Hypothetical 2018 CAT DILR Slot 1):
A company has 6 employees: A, B, C, D, E, F. They need to be assigned to 3 projects (P, Q, R) with the following constraints:
Each project must have exactly 2 employees.
A and B cannot work together.
C and D must work in the same project.
E cannot work with F.
Project P must have more experienced employees than Project Q.
Questions:
a) How many ways can the employees be assigned?
b) If experience levels are A > B > C = D > E > F, which project does C get assigned to?
Solution:
Step 1: Understand Constraints
Total Employees: 6 (A, B, C, D, E, F)
Projects: P, Q, R (each with 2 employees).
Key Constraints:
A & B cannot be together.
C & D must be together.
E & F cannot be together.
Project P > Q in experience.
Step 2: Group Employees Based on Constraints
Group 1 (Mandatory): C and D must be together. Let’s treat them as a single unit CD.
Group 2 (Cannot Pair): E and F must be separated.
Group 3 (Cannot Pair): A and B cannot be together.
Step 3: Assign Groups to Projects
Since each project needs 2 employees, and CD is a group of 2, CD must occupy one entire project. This leaves 4 employees (A, B, E, F) to fill the remaining two projects (each needing 2).
Possible Assignments for CD:
CD in Project P, Q, or R.
Case 1: CD is assigned to Project P
Remaining employees: A, B, E, F.
Split into two projects (Q and R), each with 2 employees.
Constraints:
A and B cannot be together.
E and F cannot be together.
Valid Combinations for Q and R:
Q: A & E; R: B & F
Q: A & F; R: B & E
Q: B & E; R: A & F
Q: B & F; R: A & E
Total ways for this case: 4.
Case 2: CD is assigned to Project Q
Remaining employees: A, B, E, F.
Project P must have more experienced employees than Q.
Experience order: A > B > C=D > E > F.
Since CD (C=D) are in Q, Project P must have at least one employee with higher experience than C.
Valid pairs for P: A & B, A & E, A & F, B & E, B & F, E & F (but E & F cannot be together).
Valid pairs for P: A & B, A & E, A & F, B & E, B & F.
Then R gets the remaining two.
However, A and B cannot be together. So exclude A & B.
Valid P pairs: A & E, A & F, B & E, B & F.
For each P pair, R gets the remaining two (which may violate E-F constraint).
Example: P = A & E → R = B & F (valid).
Example: P = B & F → R = A & E (valid).
Total ways for this case: 4.
Case 3: CD is assigned to Project R
Remaining employees: A, B, E, F.
No experience constraint (since P and Q are compared).
Similar to Case 1: Assign A, B, E, F to P and Q.
Valid combinations: 4 ways.
Total Assignments:
Case 1: 4
Case 2: 4
Case 3: 4
Total: 12 ways.
Step 4: Answer Question b) Experience Assignment
Given experience order: A > B > C=D > E > F.
CD is in a project. If CD is in Project Q (as in Case 2), Project P must have higher experience.
If CD is in Project P or R, the experience constraint only applies to P vs Q.
To maximize the number of valid assignments, CD is likely in Project Q to satisfy P > Q.
Thus, C and D are in Project Q.
Final Answers:
a) 12 ways
b) Project Q
Key Takeaways for CAT DILR:
Group Employees by Constraints (e.g., mandatory pairs, forbidden pairs).
Break into Cases based on fixed assignments (e.g., CD in P/Q/R).
Use经验 Order for inequalities (P > Q).
Count Valid Combinations while respecting all constraints.
Let me know if you need further clarification!
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