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Comparison Puzzle

Introduction

Comparison puzzles आपसे विभिन्न मात्राओं - ऊँचाई, अंक, वेतन, दूरी, गति आदि - की तुलना करवाते हैं। ये सटीक असमानता तर्क (>, <, ≥, ≤), ट्रांज़िटिव चेनिंग और बराबरी तथा अंतर को ध्यान से संभालने की क्षमता विकसित करते हैं।

ये पैटर्न aptitude tests और interviews में सामान्य हैं, जहाँ आपको pairwise और difference clues के आधार पर relative ordering निकालना होता है।

Pattern: Comparison Puzzle

Pattern

मुख्य विचार यह है कि मौखिक तुलना को ordered relations या inequalities में बदलें, फिर उन्हें transitively जोड़कर अंतिम रैंकिंग या संख्यात्मक उत्तर निकालें।

सामान्य संकेत: “A, B से 5 अधिक है”, “C < D < E”, “X दूसरा highest है”, या “P का वेतन Q और R के बीच है” - हर एक को symbolic relation में बदलें, फिर merge करें।

Step-by-Step Example

Question

पाँच उम्मीदवार - A, B, C, D, E - ने एक aptitude test में अलग-अलग अंक प्राप्त किए। संकेत: 1) A ने B से 8 अंक अधिक प्राप्त किए। 2) C ने D से 5 अंक कम प्राप्त किए। 3) E ने B से 3 अंक अधिक प्राप्त किए। 4) D ने A से 2 अंक अधिक प्राप्त किए। यदि B ने 62 अंक प्राप्त किए, तो सबसे अधिक किसने प्राप्त किए?

Options:

  • A) A
  • B) B
  • C) D
  • D) E

Solution

  1. Step 1: Translate numeric relations

    संकेतों से: 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

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

  5. Final Answer:

    D → Option C

  6. Quick Check:

    सभी संबंध सही: 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. शुद्ध inequality chaining (A > B = C > D).

2. अंतर-आधारित तुलना (A = B + k).

3. मिश्रित (कुछ absolute scores + relative clues)।

4. comparisons से derived rank queries (find 2nd highest / lowest)।

Trick to Always Use

  • Step 1 → हर मौखिक संकेत को एक छोटा symbolic relation में बदलें (A = B + 5, C > D, आदि)।
  • Step 2 → जब एक absolute मान दिया हो, तो numerical substitution जल्दी करें (chain को anchor मिलता है)।
  • Step 3 → एक छोटा number-line या vertical list बनाएं (top पर highest)। पहले anchored values रखें।
  • Step 4 → Quick Check: अपने final ordering से हर मूल relation को तुरंत verify करें।

Summary

Summary

  • मौखिक तुलना को तुरंत symbolic inequalities या equations में बदलें।
  • absolute anchors (दिए गए संख्यात्मक मान) पहले रखें, फिर substitution से relative values निकालें।
  • ranked list (highest → lowest) का उपयोग करें ताकि transitive chains स्पष्ट दिखें और contradictions जल्दी मिलें।
  • हमेशा एक-लाइन Quick Check करें: हर मूल संकेत को अंतिम ordering/values से जाँचें।

याद रखने योग्य उदाहरण:
B = 62, A = B + 8, D = A + 2, C = D - 5, E = B + 3 → हर मान निकालें, फिर sort करें। यहाँ D = 72 सबसे अधिक है।

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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