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Sequential or Series-Based Analogy

Introduction

Sequential அல்லது Series-Based analogies எண்கள், எழுத்துகள் அல்லது கலவை στοιங்களுக்குள் ஏற்படும் logical pattern-களை கண்டுபிடிக்கும் திறனைச் சோதிக்கின்றன. எளிய arithmetic analogies போல அல்லாமல், இங்கு இரண்டு அல்லது அதற்கும் மேற்பட்ட series-கள் ஒரே progression rule-ஐப் பின்பற்றுகிறதா என்பதை அறிதல் முக்கியம்.

Pattern: Sequential or Series-Based Analogy

Pattern

முக்கியக் கருத்து: இரு series-ங்களும் ஒரே progression rule-ஐ (arithmetic, geometric, alphabetical, alternating logic போன்றவை) பின்பற்ற வேண்டும்.

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: முதல்ஜோடியின் அமைப்பை கண்டறியுங்கள்.

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

  2. Step 2: இரு series-ங்களுக்கும் இடையிலான மாற்றத்தை கண்டுபிடிக்கவும்.

    Start +1 (2 → 3) மற்றும் difference +1 (+2 → +3).

  3. Step 3: இதே மாற்றத்தை இரண்டாவது ஜோடிக்கும் பயன்படுத்துங்கள்.

    Series2a = 5, 10, 15 → start = 5, difference = +5. Start +1 → 6; Difference +1 → +6.

  4. Final Answer:

    6, 12, 18 → Option A

  5. Quick Check:

    Start = 6, diff = +6 → 6, 12, 18. முதல்ஜோடியின் structural change-ஐ சரியாகப் பிரதிபலிக்கிறது. ✅

Quick Variations

1. Arithmetic / geometric numeric series.

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

3. Mixed logic (எண் + எழுத்து pattern, alternate arithmetic rule).

4. Increment-Decrement மாறி வரும் series.

5. Reverse / mirror progression series.

Trick to Always Use

  • Step 1 → Series numeric-ஆ, alphabetical-ஆ அல்லது mixed-ஆ என்பதை முதலில் அறிக.
  • Step 2 → சரியான rule-ஐ கண்டுபிடிக்கவும் (+, -, ×, ÷ அல்லது positional jump).
  • Step 3 → அதே pattern-ஐ missing series-க்கும் பயன்படுத்துங்கள்.
  • Step 4 → ஒவ்வொரு term-மும் ஒரே spacing / pattern-ஐப் பின்பற்றுகிறதா என சரி பார்க்கவும்.

Summary

Summary

  • Sequential analogies என்பது தனித்தெண்களை அல்ல, இரண்டு அல்லது அதற்கும் மேற்பட்ட ordered series-களை ஒப்பிடும்.
  • முதல் ஜோடியில் start மற்றும் difference/ratio எவ்வாறு அமைந்துள்ளது எனக் கண்டுபிடிக்கவும்.
  • அதே transformation-ஐ இரண்டாவது series உருவாக்கப் பயன்படுத்தவும்.
  • இரு ஜோடிகளும் ஒரே spacing மற்றும் logic-ஐ வைத்திருக்க வேண்டும்.

Example to remember:
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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