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Sequential or Series-Based Analogy

Introduction

Sequential या Series-Based Analogies यह परखती हैं कि आप किसी संख्या, अक्षर, या मिश्रित तत्वों के सेट में तार्किक पैटर्न कितनी जल्दी पहचान सकते हैं। साधारण arithmetic analogies से अलग, ये प्रश्न उसी progression नियम को दो या अधिक sequences में पहचानने और लागू करने की क्षमता माँगते हैं।

Pattern: Sequential or Series-Based Analogy

Pattern

मुख्य विचार यह है: दोनों pairs या series एक ही progression या pattern नियम का पालन करते हैं - जैसे arithmetic, geometric, alphabetical, या alternating लॉजिक।

Step-by-Step Example

Question

2, 4, 6 : 3, 6, 9 :: 5, 10, 15 : ______
(A) 6, 12, 18 (B) 7, 14, 21 (C) 8, 16, 24 (D) 9, 18, 27

Solution

  1. Step 1: पहले pair की संरचना पहचानें।

    Series1a = 2, 4, 6 → प्रारम्भ = 2, common difference = +2.
    Series1b = 3, 6, 9 → प्रारम्भ = 3, common difference = +3.

  2. Step 2: पहले pair के बीच परिवर्तन को निष्कर्षित करें।

    शुरु होने वाला पद +1 बढ़ता है (2 → 3) और common difference भी +1 बढ़ता है (+2 → +3)।

  3. Step 3: यही परिवर्तन दूसरे pair पर लागू करें।

    Series2a = 5, 10, 15 → प्रारम्भ = 5, diff = +5. अब start +1 → 6; diff +1 → +6।

  4. Final Answer:

    6, 12, 18 → Option A

  5. Quick Check:

    Series2b जहाँ start = 6 और diff = +6 होगा, वह 6, 12, 18 देता है और पहले pair जैसा structural change दर्शाता है ✅

Quick Variations

1. Numeric series जिनमें arithmetic या geometric पैटर्न हों।

2. Letter series जिनमें positional shifts हों (उदा., A, C, E → B, D, F).

3. Mixed logic (जैसे number + letter pattern, alternate arithmetic rules)।

4. Increment-Decrement alternating series।

5. Reverse या mirror sequence progressions।

Trick to Always Use

  • Step 1 → तय करें कि series numerical है, alphabetical है या mixed।
  • Step 2 → सही नियम पहचानें (+, -, ×, ÷, या positional jump)।
  • Step 3 → वही pattern missing series पर consistent रूप से लागू करें।
  • Step 4 → सत्यापित करें कि हर पद समान spacing या pattern का पालन कर रहा है।

Summary

Summary

  • Sequential analogies एक से अधिक ordered series की तुलना करते हैं, न कि केवल single values।
  • पहले pair में starting term और difference या ratio का consistent rule खोजें।
  • उसी transformation pattern को apply करके missing sequence उत्पन्न करें।
  • सुनिश्चित करें कि दोनों pairs में identical spacing और लॉजिक बनी रहे।

याद रखने के लिए उदाहरण:
2, 4, 6 : 3, 6, 9 :: 5, 10, 15 : 6, 12, 18

Practice

(1/5)
1. 3, 6, 9 : 4, 8, 12 :: 5, 10, 15 : ______
easy
A. 6, 12, 18
B. 7, 14, 21
C. 8, 16, 24
D. 9, 18, 27

Solution

  1. Step 1: Identify pattern:

    Series1a = 3, 6, 9 → start = 3, diff = +3; Series1b = 4, 8, 12 → start = 4, diff = +4.

  2. Step 2: Apply rule:

    The rule is start +1 and diff +1.

  3. Step 3: Compute new series:

    Series2a = 5, 10, 15 → start = 5, diff = +5 → apply start +1 = 6; diff +1 = +6 → 6, 12, 18.

  4. Final Answer:

    6, 12, 18 → Option A

  5. Quick Check:

    Same structural rule (Start +1, Diff +1) holds ✅
Hint: When both sequences are arithmetic, compare the first term and difference.
Common Mistakes: Confusing common difference with a multiplication rule.
2. A, C, E : B, D, F :: P, R, T : ______
easy
A. Q, S, U
B. O, Q, S
C. R, T, V
D. S, U, W

Solution

  1. Step 1: Identify pattern:

    A, C, E → alternate letters (+2 jump each). B, D, F → same pattern, starting one ahead.

  2. Step 2: Apply rule:

    P, R, T → +2 pattern, so start one ahead (Q) and continue same +2 pattern → Q, S, U.

  3. Final Answer:

    Q, S, U → Option A

  4. Quick Check:

    A→B (+1 start), same pattern applied ✅
Hint: For alphabetic series, note the skip count between letters.
Common Mistakes: Starting from wrong letter or using wrong letter gap.
3. 1, 3, 5, 7 : 2, 4, 6, 8 :: 10, 12, 14, 16 : ______
easy
A. 11, 13, 15, 17
B. 12, 14, 16, 18
C. 13, 15, 17, 19
D. 9, 11, 13, 15

Solution

  1. Step 1: Identify pattern:

    1,3,5,7 (odd numbers) → 2,4,6,8 (even numbers next to each).

  2. Step 2: Apply rule:

    10,12,14,16 (even numbers) → add +1 to each to get next odd sequence.

  3. Step 3: Compute new series:

    10 +1 = 11, 12 +1 = 13, 14 +1 = 15, 16 +1 = 17 → 11,13,15,17.

  4. Final Answer:

    11, 13, 15, 17 → Option A

  5. Quick Check:

    Even → next odd pattern applied ✅
Hint: When one series converts odd to even, apply the same parity logic.
Common Mistakes: Adding +2 instead of +1 to each term.
4. 5, 10, 20 : 10, 20, 40 :: 7, 14, 28 : ______
medium
A. 8, 16, 32
B. 9, 18, 36
C. 14, 28, 56
D. 15, 30, 60

Solution

  1. Step 1: Identify pattern:

    First pair: each term doubles (×2 rule). 5→10→20 and 10→20→40 both follow ×2.

  2. Step 2: Apply rule:

    Apply same logic to 7,14,28; next sequence must double.

  3. Step 3: Compute new series:

    7×2 = 14, 14×2 = 28, 28×2 = 56 → 14,28,56.

  4. Final Answer:

    14, 28, 56 → Option C

  5. Quick Check:

    ×2 rule holds consistently ✅
Hint: Look for consistent multiplication ratios in geometric progressions.
Common Mistakes: Adding instead of multiplying.
5. 2, 5, 10 : 5, 10, 17 :: 3, 8, 15 : ______
medium
A. 6, 13, 22
B. 8, 15, 24
C. 7, 14, 23
D. 9, 16, 25

Solution

  1. Step 1: Identify the pattern in the first pair

    First series: 2, 5, 10 → differences are +3, +5. Next series: 5, 10, 17 → differences are +5, +7. The pattern shows each new series starts from the second term of the previous series, and the internal differences increase by +2 each time (+3 → +5 → +7).

  2. Step 2: Apply the same rule to the second pair

    Second given series: 3, 8, 15 → differences are +5, +7. Following the same logic, the next series will start from the 2nd term (8), then 3rd term (15), and the next term should be 15 + 9 = 24.

  3. Step 3: Construct the new sequence

    Therefore, the new sequence is 8, 15, 24.

  4. Final Answer:

    8, 15, 24 → Option B

  5. Quick Check:

    Each new series continues from the previous one, maintaining +2 growth in internal differences ✅
Hint: Notice that each new series begins with the middle term of the previous one and continues with growing odd-number differences (+3, +5, +7, +9).
Common Mistakes: Treating the series as a simple arithmetic progression instead of recognizing the overlapping and increasing-difference pattern.

Mock Test

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