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About Logical Reasoning — Class 9 Olympiad

Solve analogy, classification, coding-decoding, number series, figure patterns, direction sense, Venn diagrams, mirror images, and paper folding problems. This topic is part of the Olympiad Class 9 mathematics syllabus (chapter: Module 12). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Logical Reasoning — solved examples for Class 9 Olympiad

Example 1easy

If 9 is to 90 as 13 is to 182, then 17 is to ?
  1. A)A. 288
  2. B)B. 306
  3. C)C. 324
  4. D)D. 342

Step-by-step solution

  1. Observe the first pair: 9 and 90. The relationship is 9 × (9 + 1) = 9 × 10 = 90.
  2. Verify with the second pair: 13 and 182. The relationship is 13 × (13 + 1) = 13 × 14 = 182.
  3. Apply the same logic to the third number, 17: 17 × (17 + 1) = 17 × 18 = 306.

Answer: B. 306

Example 2medium

If the analogy '5 : 130 :: 7 : X' holds true, what is the value of X?
  1. A)343
  2. B)350
  3. C)357
  4. D)364

Step-by-step solution

  1. Analyze the first pair: 5 : 130.
  2. Observe that 130 can be expressed as 5³ + 5. (5³ = 125, so 125 + 5 = 130).
  3. Apply the same rule to the second pair: 7 : X.
  4. Therefore, X = 7³ + 7 = 343 + 7 = 350.

Answer: 350

Example 3hard

If 12 : 78, then 18 : ?
  1. A)162
  2. B)171
  3. C)180
  4. D)189

Step-by-step solution

  1. Analyze the given relationship: 12 : 78.
  2. We observe that 78 can be obtained from 12 by the formula: (n/2) × (n+1).
    Forn=12:(12/2)×(12+1)=6×13=78.For n = 12: (12/2) × (12+1) = 6 × 13 = 78.
  3. Apply the same rule for n = 18.
    Forn=18:(18/2)×(18+1)=9×19=171.For n = 18: (18/2) × (18+1) = 9 × 19 = 171.

Answer: 171

Practice questions on Logical Reasoning

  1. Q1.easy

    Which of the following numbers is the odd one out?
    1. A)A. 1331
    2. B)B. 2197
    3. C)C. 4913
    4. D)D. 5832
    Show answer

    Answer: D. 5832

    Hint: Consider the properties of the base numbers when these given numbers are expressed as cubes.

  2. Q2.easy

    In a certain code, 'PRIME' is written as 'TULPH'. How is 'NUMBER' written in that same code?
    1. A)A. RXPEHU
    2. B)B. RXPFHV
    3. C)C. SWQEIT
    4. D)D. VZQGIW
    Show answer

    Answer: A. RXPEHU

    Hint: Analyze the shift in alphabetical position for each letter from 'PRIME' to 'TULPH'. The shift might not be uniform for all letters.

  3. Q3.easy

    What is the next term in the series: 7, 18, 32, 49, 69, ?
    1. A)A. 89
    2. B)B. 92
    3. C)C. 95
    4. D)D. 98
    Show answer

    Answer: B. 92

    Hint: Calculate the differences between consecutive terms and look for a pattern in this new sequence of differences.

  4. Q4.medium

    Which of the following numbers is the odd one out?
    1. A)676
    2. B)729
    3. C)784
    4. D)841
    Show answer

    Answer: 729

    Hint: Consider the properties of each number. Are they perfect squares, perfect cubes, or both?

  5. Q5.medium

    In a certain code, 'ACE' is coded as '6' and 'BDF' is coded as '12'. How would 'CEG' be coded?
    1. A)9
    2. B)10
    3. C)12
    4. D)15
    Show answer

    Answer: 10

    Hint: Consider the alphabetical position of each letter. The code might involve an average or sum of these positions combined with the number of letters.

  6. Q6.medium

    What is the next number in the series: 1, 2, 6, 21, 88, X?
    1. A)440
    2. B)445
    3. C)450
    4. D)455
    Show answer

    Answer: 445

    Hint: Look for a recursive pattern where each term depends on its position in the series and the previous term.

  7. Q7.hard

    Find the number that does not belong to the group.
    1. A)1331
    2. B)2197
    3. C)4913
    4. D)729
    Show answer

    Answer: 729

    Hint: Examine the fundamental properties of the roots of these numbers.

  8. Q8.hard

    If SOF is coded as 58, then what is IMO coded as?
    1. A)54
    2. B)55
    3. C)56
    4. D)57
    Show answer

    Answer: 55

    Hint: Assign numerical values to letters (A=1, B=2, ...) and look for a pattern involving the sum of these values and the number of letters in the word.

  9. Q9.hard

    What is the next term in the series: 2, 7, 26, 107, ?
    1. A)428
    2. B)431
    3. C)540
    4. D)542
    Show answer

    Answer: 540

    Hint: Look for a recursive relationship where the current term depends on the previous term, and both the multiplier and additive constant follow specific patterns.

These are 9 of the 59 questions available for Logical Reasoning. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.