Comparison Ordering — Taller, Older, Heavier

🎯 Learning Objective

Turn taller/shorter and older/younger statements into one ordered chain and read off any rank.

💡 Concept

• Turn every statement into a chain with > signs, keeping the taller/older/heavier side on the LEFT
• 'A is taller than B' → A > B; 'A is older than B' → A > B (by age)
• 'A is taller than B but shorter than C' compresses in one go to C > A > B
• Merge chains through the common name until everyone sits in one single line
• Middle of 5 people = 3rd position; middle of 7 = 4th — and re-read which rank is asked

🧮 Key Formulas

'A > B but A < C' → C > A > B

>

Middle of 5 = 3rd, middle of 7 = 4th

✏️ Easy Example

Q. Ankit is taller than Bharat. Chirag is taller than Ankit. Who is the tallest of the three?

1. Ankit > Bharat, and Chirag > Ankit
2. Merge through Ankit: Chirag > Ankit > Bharat

Answer: Chirag

🇮🇳 Real-Life Example

After every match you rank batsmen without thinking — 'Gill made more than Rohit but less than Kohli.' Building that score chain IS comparison ordering.

📝 Exam-Level Example

Q. P is taller than Q but shorter than R. S is taller than R. T is shorter than Q. Who is in the middle when they stand tallest to shortest?

1. P > Q and R > P → R > P > Q
2. S > R → S > R > P > Q
3. T < Q → S > R > P > Q > T
4. Middle of 5 (3rd) = P

Answer: P

📝 Exam-Level Example

Q. Amit is older than Bhavya. Chetan is younger than Bhavya. Deepak is older than Amit. Esha is younger than Chetan. Who is the second oldest?

1. Amit > Bhavya and Bhavya > Chetan → Amit > Bhavya > Chetan
2. Deepak > Amit → Deepak > Amit > Bhavya > Chetan
3. Esha < Chetan → Deepak > Amit > Bhavya > Chetan > Esha
4. Oldest = Deepak, so second oldest = Amit

Answer: Amit

🪄 Memory Trick

One line, arrows one way — keep the bigger side on the left always. Build the chain once and every sub-question (tallest, youngest, middle, 2nd) comes free.

⚠️ Common Mistakes

• ❌ Flipping the chain direction halfway through
• ❌ Misreading 'younger than' or 'shorter than' inside a long sentence
• ❌ Answering the tallest when the middle or 2nd is asked

🏆 Exam Tips

• ✅ Rewrite every 'X but Y' statement as a 3-name chain in one go
• ✅ After merging, count heads — every name must appear exactly once

📌 Summary

• Convert each statement into a > chain, bigger on the left
• Merge through common names into one line
• Middle of 5 = 3rd, of 7 = 4th
• Re-read exactly which rank the question wants