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Comparison Puzzle

Introduction

Comparison puzzles ask you to compare quantities - heights, marks, salaries, distances, speeds, etc. They train precise inequality reasoning (>, <, ≥, ≤), transitive chaining, and careful handling of equalities and differences.

These patterns are common in aptitude tests and interviews where you must deduce relative ordering from pairwise and difference clues.

Pattern: Comparison Puzzle

Pattern

The key idea is to convert verbal comparisons into ordered relations or inequalities and then chain them transitively to get the final ranking or numeric answer.

Typical clue types: “A is greater than B by 5”, “C < D < E”, “X is the second highest”, or “P’s salary is between Q and R”. Convert each into a symbolic relation first, then merge.

Step-by-Step Example

Question

Five candidates - A, B, C, D, E - scored different marks in an aptitude test. Clues: 1) A scored 8 marks more than B. 2) C scored 5 marks less than D. 3) E scored 3 marks more than B. 4) D scored 2 marks more than A. If B scored 62 marks, who scored the highest?

Options:

  • A) A
  • B) B
  • C) D
  • D) E

Solution

  1. Step 1: Translate numeric relations

    From clues: A = B + 8; E = B + 3; D = A + 2; C = D - 5.

  2. Step 2: Substitute B = 62

    B = 62 → A = 62 + 8 = 70; E = 62 + 3 = 65.

  3. Step 3: Get D and C

    D = A + 2 = 70 + 2 = 72. C = D - 5 = 72 - 5 = 67.

  4. Step 4: Order the marks

    Marks (highest → lowest): D (72), A (70), C (67), E (65), B (62).

  5. Final Answer:

    D → Option C

  6. Quick Check:

    All relations satisfied: A = B + 8 (70 = 62 + 8) ✅ D = A + 2 (72 = 70 + 2) ✅ C = D - 5 (67 = 72 - 5) ✅ E = B + 3 (65 = 62 + 3) ✅

Quick Variations

1. Pure inequality chaining (A > B = C > D).

2. Difference-based comparisons (A = B + k).

3. Mixed (some absolute scores given + relative clues).

4. Rank queries derived from comparisons (find 2nd highest / lowest).

Trick to Always Use

  • Step 1 → Convert every verbal clue into a short symbolic relation (A = B + 5, C > D, etc.).
  • Step 2 → Use numerical substitution early when one absolute value is provided (anchors the chain).
  • Step 3 → Draw a quick number-line or vertical list (highest at top) and place anchored values first.
  • Step 4 → Re-check each original relation against your final ordering immediately (Quick Check).

Summary

Summary

  • Convert verbal comparisons into symbolic inequalities or equations immediately.
  • Place absolute anchors (given numeric values) first, then propagate relative values by substitution.
  • Use a ranked list (highest → lowest) to visualize transitive chains and spot contradictions early.
  • Always perform a one-line Quick Check: verify every original clue against the final ordering/numbers.

Example to remember:
Given B = 62, A = B + 8, D = A + 2, C = D - 5, E = B + 3 → compute each, then sort. Here D = 72 is highest.

Practice

(1/5)
1. Five persons - P, Q, R, S, and T - earn different monthly salaries. Q earns ₹5,000 more than P, but ₹3,000 less than R. T earns ₹4,000 more than S. R earns more than T. If P earns ₹40,000, who earns the highest salary?
easy
A. R
B. Q
C. T
D. S

Solution

  1. Step 1: Assign base salaries

    P = ₹40,000 → Q = ₹45,000 → R = ₹48,000.

  2. Step 2: Express T and S

    T = S + ₹4,000 (no direct number for S).

  3. Step 3: Apply the added constraint R > T

    R > T ⇒ 48,000 > S + 4,000 ⇒ S < ₹44,000 ⇒ T < ₹48,000.

  4. Step 4: Compare all

    R = ₹48,000 is higher than Q = ₹45,000 and P = ₹40,000. T and S are both below ₹48,000. Thus, R is uniquely highest.

  5. Final Answer:

    R → Option A
Hint: Use the extra comparison (R > T) to lock the chains together and remove ambiguity.
Common Mistakes: Missing the R > T condition, which makes T appear potentially highest.
2. Five students - A, B, C, D, and E - scored different marks. A scored 5 marks less than B, but 10 marks more than C. D scored 3 marks more than B. Who scored the second highest?
easy
A. B
B. D
C. A
D. C

Solution

  1. Step 1: Represent scores symbolically

    Let C = x. Then A = x + 10; B = A + 5 = x + 15; D = B + 3 = x + 18.

  2. Step 2: Arrange in descending order

    D (x + 18) > B (x + 15) > A (x + 10) > C (x).

  3. Step 3: Identify the second highest

    Second highest = B.

  4. Final Answer:

    B → Option A

  5. Quick Check:

    D > B > A > C ✅
Hint: Always anchor one variable as the lowest score and express others relative to it.
Common Mistakes: Swapping the direction of 'less than' or 'more than'.
3. In a race, P ran faster than Q but slower than R. S ran slower than Q. Who is the second fastest?
easy
A. P
B. Q
C. R
D. S

Solution

  1. Step 1: Translate speed relations

    P faster than Q ⇒ P > Q; P slower than R ⇒ R > P; S slower than Q ⇒ Q > S.

  2. Step 2: Combine inequalities

    R > P > Q > S.

  3. Step 3: Identify ranks

    Fastest = R; Second fastest = P.

  4. Final Answer:

    P → Option A

  5. Quick Check:

    Chain R > P > Q > S holds correctly ✅
Hint: Convert all comparative words ('faster', 'slower') into inequality signs before chaining.
Common Mistakes: Reversing the inequality direction while forming the chain.
4. Four boxes - A, B, C, and D - have different weights. A is heavier than B but lighter than C. D is lighter than B. Which box is the lightest?
medium
A. B
B. C
C. D
D. A

Solution

  1. Step 1: Write inequalities

    A > B but A < C ⇒ C > A > B.

  2. Step 2: Add remaining condition

    D < B ⇒ D is lighter than all.

  3. Step 3: Order from heaviest to lightest

    C > A > B > D.

  4. Final Answer:

    D → Option C

  5. Quick Check:

    Every comparison holds true ✅
Hint: Start from the given 'middle' object and expand relations both up and down.
Common Mistakes: Confusing 'lighter' and 'heavier' relation directions.
5. Four friends - J, K, L, and M - have different heights. K is taller than J but shorter than L. M is shorter than K. Who is the tallest?
medium
A. K
B. L
C. M
D. J

Solution

  1. Step 1: Build inequality chain

    K > J and K < L ⇒ L > K > J.

  2. Step 2: Add the final comparison

    M < K ⇒ L > K > J > M.

  3. Step 3: Determine tallest

    Tallest = L.

  4. Final Answer:

    L → Option B

  5. Quick Check:

    Heights follow L > K > J > M ✅
Hint: Always combine all inequalities into a single ordered chain before answering.
Common Mistakes: Ignoring one condition when building the chain.

Mock Test

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