CAT Logical Reasoning: Puzzle Set

Complex logical reasoning puzzle involving multiple variables and conditions.

# Aplly.xyz Case Study Submission

## Title
CAT Logical Reasoning: Puzzle Set

## Type
CAT / Competitive Aptitude

## Difficulty
Intermediate

## Estimated Time
60 minutes

## Overview
Complex logical reasoning puzzle involving multiple variables and conditions.

## Case Details

Function Focus: CAT / Competitive Aptitude — manual reasoning, decomposition, and critical judgment (no spreadsheet or AI tool permitted in Phase 1)

Scenario:
You are the analyst at a fictional consultancy ("Praxis Advisors") tasked with answering: CAT Logical Reasoning: Puzzle Set. You have a clean, synthetic dataset described below. You must produce a defensible answer using structured reasoning — no tool-assisted shortcut on the first pass.

Dataset Structure:
- puzzle_id
- type
- clue_1
- clue_2
- clue_3
- clue_4
- entities
- arrangements

Tasks:
1. Solve the first question by hand using the standard formula; write every intermediate step.
2. For the second question, attempt a logical elimination approach before any calculation shortcut.
3. Use approximation/estimation to sanity-check your answer; state your rounding assumptions.
4. Identify the most time-efficient solving order for the set and justify it.
5. Verify your answers with a calculator or spreadsheet and mark any error you made in the manual pass.

Expected Output:
A solved answer sheet with all steps shown, final answers, time taken, and a short self-review note.

Evaluation Criteria:
Accuracy and completeness of steps, correct formula application, efficient solving order, honesty in self-review.

## Data Sources

| puzzle_id | type | clue_1 | clue_2 | clue_3 | clue_4 | entities | arrangements |
|---|---|---|---|---|---|---|---|
| P001 | Seating | A sits 3-left of B | C is opposite D | E at extreme left | F adjacent to G | A,B,C,D,E,F,G,H | 8 seats circular |
| P002 | Bloodline | P is Q's father | R is S's sister | T is P's wife | U is R's daughter | P,Q,R,S,T,U | Family tree |
| P003 | Scheduling | Meeting M at 10am | N before O | P after Q | R at 2pm | M,N,O,P,Q,R | 6 time slots |
| P004 | Inequality | A > B > C | D < E | F > A | G < C > H | A,B,C,D,E,F,G,H | 8 variables |
| P005 | Coding | APPLE = BNQMF | MANGO = NBNHP | BANANA = CBOBOB | GRAPE = HSBQF | APPLE,MANGO,BANANA,GRAPE | Letter shift |
| P006 | Seating | X is 2-right of Y | Z between W and V | U opposite T | S left of R | R,S,T,U,V,W,X,Y,Z | 9 seats linear |
| P007 | Bloodline | A is B's brother-in-law | C is D's mother | E is F's granddaughter | G is H's uncle | A,B,C,D,E,F,G,H | Family tree |
| P008 | Distribution | Red = 2x Blue | Green = Red + 3 | Total < 30 | Blue > Yellow | Red,Blue,Green,Yellow | 4 colors |
| P009 | Direction | P walks 5km N then 3km E | Q walks 4km S then 6km W | R walks 2km E then 7km N | Dist P-Q = ? | P,Q,R | Coordinate grid |
| P010 | Analogy | Doctor:Hospital :: Teacher:? | Pencil:Write :: Brush:? | Tree:Forest :: Star:? | Book:Chapter :: House:? | all | 10 analogies |


Full dataset: https://github.com/arora200/aplly_case_db/datasets/043-cat-logical-reasoning-puzzles (synthetic, 10 records)

## Solution Frameworks
Formula-based quantitative solving, structured logical elimination, approximation & estimation, time-management heuristics

## Solver Guidance & Tutorials
_Solver guidance added by the pipeline (tutorial links) — see `solver_guidance` field._

## What You'll Learn
- Solve quantitative problems step-by-step by hand
- Choose the fastest solving order
- Self-check answers with estimation

## Tags
CAT, Logical Reasoning, Puzzle

## Registration Links
Register as Solver / Register as Evaluator