How to Solve: CUET Reasoning – Ranking and Ordering

How to Solve: CUET Reasoning – Ranking and Ordering

Introduction

"Imagine you’re in a race with 50 runners, and you only know who finished 3rd and 5th—but the exam asks for your exact position. Master ranking and ordering, and you’ll crack this in under 60 seconds."

What You Need To Know First

1. Basic inequalities (>, <, =) – You must know how to compare numbers.
2. Position vs. Rank – Position is a fixed spot (e.g., 1st, 2nd); rank can change based on criteria.
3. Left/Right vs. Top/Bottom – Directions matter in seating/ranking problems.

Key Vocabulary

Formulas To Know

1. Finding Position from One End

Formula: Position from other end = Total positions + 1 – Position from given end

Variables: - Total positions = Total number of items (e.g., seats, ranks). - Position from given end = Known position (e.g., 3rd from left).

Example: If 10 people sit in a row and A is 3rd from the left, A’s position from the right = 10 + 1 – 3 = 8th.

MEMORISE THIS – Not given on the exam sheet.

2. Finding Total Positions When Two Positions Are Given

Formula: Total positions = (Position from left + Position from right) – 1

Variables: - Position from left = Rank from the left end. - Position from right = Rank from the right end.

Example: If X is 4th from the left and 3rd from the right in a row, total positions = (4 + 3) – 1 = 6.

MEMORISE THIS – Not given on the exam sheet.

3. Finding Gaps Between Two People

Formula: Number of people between A and B = |Position of A – Position of B| – 1

Variables: - | | = Absolute value (ignore negative signs). - Position of A/B = Their rank in the sequence.

Example: If A is 2nd and B is 5th, people between them = |5 – 2| – 1 = 2.

MEMORISE THIS – Not given on the exam sheet.

Step-by-Step Method

Step 1: Read the Question Twice

• Underline key words (e.g., "immediately," "between," "total").
• Circle numbers (e.g., "3rd from left," "5 people").

Step 2: Draw a Blank Line for the Sequence

• Example: _ _ _ _ _ (for 5 positions).
• Label ends (Left/Right or Top/Bottom).

Step 3: Fill in Fixed Positions First

• If someone is "3rd from the left," write their name in the 3rd blank.
• If someone is "immediately above," place them right next to the reference.

Step 4: Use Formulas for Unknowns

• Apply the position from other end or total positions formula if needed.
• Example: If A is 2nd from left in a row of 7, A is (7 + 1 – 2) = 6th from right.

Step 5: Check for Hidden Clues

• Words like "only," "exactly," or "not" change meanings.
• Example: "Only 2 people are between A and B" = |A – B| – 1 = 2.

Step 6: Verify with All Given Conditions

• Cross-check every clue in the question.
• If a condition fails, redo Step 3.

Step 7: Answer the Specific Question

• Don’t assume! The question might ask for:
• A person’s position.
• Number of people between two.
• Total positions in the sequence.

Worked Examples

Example 1 – Basic

Question: In a row of 8 people, A is 3rd from the left. What is A’s position from the right?

Step-by-Step Solution: 1. Total positions = 8. 2. A’s position from left = 3. 3. Use formula: Position from right = Total + 1 – Position from left. 4. Calculation: 8 + 1 – 3 = 6. 5. Answer: A is 6th from the right.

What we did and why: We used the position from other end formula because the question gave one position and asked for the opposite end.

Example 2 – Medium

Question: In a row, P is 5th from the left and 6th from the right. How many people are in the row?

Step-by-Step Solution: 1. P’s position from left = 5. 2. P’s position from right = 6. 3. Use formula: Total positions = (Left position + Right position) – 1. 4. Calculation: (5 + 6) – 1 = 10. 5. Answer: There are 10 people in the row.

What we did and why: We used the total positions formula because two positions (left and right) were given for the same person.

Example 3 – Exam Style

Question: Six people – A, B, C, D, E, F – sit in a row from left to right. A is to the left of B. C is immediately to the right of D. E is 2nd from the left. F is not at either end. Who is 3rd from the right?

Step-by-Step Solution: 1. Draw 6 blanks: _ _ _ _ _ _. 2. E is 2nd from left → _ E _ _ _ _. 3. A is left of B → A must be before B (order unknown yet). 4. C is immediately right of D → D C (must be together). 5. F is not at ends → F cannot be 1st or 6th. 6. Possible positions for D C:
- If D C in 3-4: _ E D C _ _ → F must be 5th (only non-end spot left).
- Then A and B must be 1st and 6th (but 6th is an end, and F can’t be there). Invalid.
- If D C in 4-5: _ E _ D C _ → F must be 1st or 6th (but 6th is an end). Invalid.
- If D C in 1-2: D C E _ _ _ → But E is 2nd from left. Invalid.
- Correct: D C in 5-6: _ E _ _ D C → F must be 3rd (only non-end spot left).
- Then A and B must be 1st and 4th.
- A is left of B → A is 1st, B is 4th. 7. Final order: A E F B D C. 8. 3rd from right = 4th from left = B.

What we did and why: We used process of elimination and fixed positions (E, D C) to narrow down possibilities. The key was testing D C’s placement and ensuring F wasn’t at the ends.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, last-minute cram for CUET Ranking and Ordering! Here’s the cheat code:

1. Draw blanks – Always sketch the sequence first.
2. Fill fixed positions – If someone is 3rd from left, write their name in the 3rd blank.
3. Use the formulas –
4. Position from other end? Total + 1 – Given position.
5. Total positions? (Left + Right) – 1.
6. People between two? |A – B| – 1.
7. Watch for traps – "Immediately" means no gaps, "not at ends" means cross out first/last.
8. Double-check – Every clue must fit before you bubble the answer.

You’ve got this. Now go ace that exam!

Final Note for Teachers: - Pacing: Spend 2 minutes on formulas, 5 minutes on worked examples, 2 minutes on common mistakes. - Visuals: Use a whiteboard to draw blanks and fill them step-by-step. - Engagement: Ask students, "What’s the first thing you’d write down for this question?" to reinforce Step 1.