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Ranking and Order Based Data Sufficiency

Introduction

Ranking & Order Data Sufficiency उन प्रश्नों से संबंधित है जिनमें यह पता करना होता है कि क्या दिए गए statements किसी व्यक्ति की rank/position (top या bottom से), कुल लोगों की संख्या, या relative ordering को निर्धारित करने के लिए पर्याप्त जानकारी देते हैं। ये problems positional relations को equations में बदलने और result की uniqueness जाँचने की आपकी क्षमता परखेते हैं।

यह pattern महत्वपूर्ण है क्योंकि कई competitive exams short statements में ranking facts देते हैं; आपको तय करना होता है कि क्या हर statement अकेला पर्याप्त है या दोनों मिलकर ही unique answer देते हैं।

Pattern: Ranking and Order Based Data Sufficiency

Pattern

मुख्य concept यह है: positional statements को इस तरह के equations में बदलें - rank_from_top + rank_from_bottom = total + 1 - और relative relations (जैसे "X is 3rd from the top", "Y is two places after X") को constraints में बदलकर देखें कि क्या वे requested quantity को uniquely तय करते हैं।

Step-by-Step Example

Question

क्लास में कुल कितने students हैं?
(I) Raj top से 8वाँ है।
(II) Raj bottom से 13वाँ है।

A. केवल (I) पर्याप्त है
B. केवल (II) पर्याप्त है
C. प्रत्येक statement अकेला पर्याप्त है
D. दोनों statements साथ में आवश्यक हैं

Solution

  1. Step 1: Statement (I) का अर्थ समझें

    Raj = top से 8वाँ। यह Raj की top से position देता है पर total students नहीं बताता → (I) अकेला insufficient है।

  2. Step 2: Statement (II) का अर्थ समझें

    Raj = bottom से 13वाँ। यह Raj की bottom से position देता है पर total नहीं → (II) अकेला insufficient है।

  3. Step 3: Combine करें

    नीचे दिए हुए identity का उपयोग करें: rank_from_top + rank_from_bottom = total + 1.
    8 + 13 = total + 1 ⇒ total = 8 + 13 - 1 = 20.

  4. Final Answer:

    दोनों statements साथ में आवश्यक हैं → Option D

  5. Quick Check:

    अगर total = 20 है तो Raj top से 8वाँ और bottom से 13वाँ होगा (8 + 13 = 21 = 20 + 1) ✅

Quick Variations

1. एक statement top से rank देता है और दूसरा bottom से - इन्हें जोड़ने के लिए rank_from_top + rank_from_bottom = total + 1 इस्तेमाल करें।

2. Statements में relative positions दिए हों (जैसे "A is 3 places ahead of B") - इन्हें constraints में बदलें और uniqueness चेक करें।

3. Statements partial ordering दें (जैसे "A is above B, C is below B") - exact rank के लिए अतिरिक्त जानकारी की जरूरत पड़ सकती है।

4. कभी-कभी पूछा गया target किसी व्यक्ति की position होता है और कभी कुल संख्या - पहले target स्पष्ट कर लें क्योंकि अलग formulas लागू होते हैं।

Trick to Always Use

  • Step 1: तय करें कि target rank (position) है या total count।
  • Step 2: "from top/from bottom" को numeric positions में बदलें और identity top + bottom = total + 1 का उपयोग करें जहाँ लागू हो।
  • Step 3: relative statements ("X is k places after Y", "between", "immediately left/right") को equations या inequalities में translate करें।
  • Step 4: uniqueness चेक करें: अगर equations target के लिए single numeric value देती हैं तो statement(s) sufficient हैं; नहीं तो insufficient हैं।

Summary

Summary

  • Positional शब्दों को numbers में बदलें और जब top और bottom दोनों positions मिले तो rank_from_top + rank_from_bottom = total + 1 का प्रयोग करें।
  • Relative positions को equations में ट्रांसलेट करें (उदा., A = B + k जब "A is k places after B" कहा हो)।
  • पहले target (rank बनाम total) निर्धारित करें - अलग लक्ष्यों के लिए अलग formulas होते हैं।
  • Uniqueness verify करें: अगर statements से एक consistent numeric value आती है तो sufficient; अगर degrees of freedom या contradiction रह जाती है तो insufficient।

याद रखने के लिए उदाहरण:
यदि X top से 5वाँ और bottom से 7वाँ है, तो total = 5 + 7 - 1 = 11।

Practice

(1/5)
1. What is Karan's rank from the top?<br>(I) Karan is 5th from the top.<br>(II) There are 30 students in the class.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    (I) directly gives Karan's rank from top = 5th → (I) alone is sufficient.

  2. Step 2: Analyze (II)

    (II) gives total = 30 but no position of Karan → (II) alone is insufficient.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    (I) already provides the required rank (5th) ✅
Hint: If a statement directly gives the required rank, it is sufficient by itself.
Common Mistakes: Trying to use total count without a positional clue.
2. What is Meera's rank from the bottom?<br>(I) Meera is 6th from the top.<br>(II) Meera is 15th from the bottom.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    (I) gives Meera = 6th from top → bottom rank needs total, so (I) alone is insufficient.

  2. Step 2: Analyze (II)

    (II) directly gives Meera = 15th from bottom → (II) alone is sufficient.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    (II) provides the required bottom rank directly ✅
Hint: A statement that directly states the asked-from position is sufficient.
Common Mistakes: Assuming top rank alone gives bottom rank without total.
3. What is Nitin's rank from the top?<br>(I) Nitin is 3rd from the top.<br>(II) There are 10 students and Nitin is 8th from the bottom.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    (I) gives Nitin = 3rd from top → (I) alone is sufficient.

  2. Step 2: Analyze (II)

    (II) gives total = 10 and Nitin = 8th from bottom. Top rank = total + 1 - bottom = 10 + 1 - 8 = 3rd from top → (II) alone is also sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    Both (I) and (II) independently yield Nitin = 3rd from top ✅
Hint: Convert bottom → top via top = total + 1 - bottom when total is given.
Common Mistakes: Failing to convert bottom rank to top rank when total is known.
4. How many students are there in the class?<br>(I) Asha is 7th from the top.<br>(II) Asha is 10th from the bottom.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    (I) gives Asha = 7th from top → total unknown → insufficient.

  2. Step 2: Analyze (II)

    (II) gives Asha = 10th from bottom → total unknown → insufficient.

  3. Step 3: Combine

    Use top + bottom = total + 1 ⇒ 7 + 10 = total + 1 ⇒ total = 7 + 10 - 1 = 16.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    7 + 10 - 1 = 16 ⇒ positions consistent ✅
Hint: When you have both top and bottom ranks for the same person, use top + bottom - 1 = total.
Common Mistakes: Using one rank alone to infer total.
5. How many students are between Dev and Esha?<br>(I) Dev is 4th from the top and Esha is 9th from the top.<br>(II) There are 20 students in the class.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Dev = 4th, Esha = 9th from top → number between = 9 - 4 - 1 = 4 → (I) alone is sufficient.

  2. Step 2: Analyze (II)

    Total = 20 gives no direct positions → (II) alone is insufficient.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    Positions 4 and 9 ⇒ 9 - 4 - 1 = 4 between them ✅
Hint: Number between two top ranks = larger rank - smaller rank - 1.
Common Mistakes: Forgetting to subtract 1 when counting people between two ranks.

Mock Test

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