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About Logical Reasoning — Class 7 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 7 mathematics syllabus (chapter: Module 14). 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 7 Olympiad

Example 1easy

Find the missing number in the analogy: 12 : 144 :: 17 : ?
  1. A)196
  2. B)289
  3. C)324
  4. D)361

Step-by-step solution

  1. In the first pair, 12 : 144, we observe that 144 is the square of 12 (12 × 12 = 144).
  2. Therefore, to find the missing number, we apply the same rule to the second pair.
  3. For 17 : ?, we need to find the square of 17.
  4. 17 × 17 = 289.

Answer: 289

Example 2medium

If 12 : 1440 :: 15 : ?
  1. A)2925
  2. B)3000
  3. C)2850
  4. D)3100

Step-by-step solution

  1. For the first pair, 12 : 1440.
  2. Observe the pattern: 1440 = 12 × 120. Also, 120 can be written as 12 × 10. So, 1440 = 12 × 12 × 10 = 12^2 × 10.
  3. The factor '10' can be derived from the number 12 as (12 - 2). Thus, the pattern is N : N^2 × (N - 2).
  4. Applying this to 15: 15^2 × (15 - 2) = 225 × 13 = 2925.

Answer: 2925

Example 3hard

If 'MATH' is coded as 'NCWL' and 'LOGIC' is coded as 'MQJMH', how would 'SCIENCE' be coded using the same logic?
  1. A)TELISIL
  2. B)TDKHQJI
  3. C)TFLISTL
  4. D)UESJTLM

Step-by-step solution

  1. The coding rule is that each letter is shifted forward in the alphabet by a number equal to its position in the word. The 1st letter shifts by 1, the 2nd by 2, the 3rd by 3, and so on.
  2. Let's verify with 'MATH': M(13)+1=N(14), A(1)+2=C(3), T(20)+3=W(23), H(8)+4=L(12). This correctly gives 'NCWL'.
  3. Applying this to 'SCIENCE': S(19)+1=T(20), C(3)+2=E(5), I(9)+3=L(12), E(5)+4=I(9), N(14)+5=S(19), C(3)+6=I(9), E(5)+7=L(12).
  4. Thus, 'SCIENCE' is coded as 'TELISIL'.

Answer: TELISIL

Practice questions on Logical Reasoning

  1. Q1.easy

    Choose the word that is different from the others:
    (A) RIVER
    (B) LAKE
    (C) POND
    (D) MOUNTAIN
    1. A)RIVER
    2. B)LAKE
    3. C)POND
    4. D)MOUNTAIN
    Show answer

    Answer: MOUNTAIN

    Hint: Consider the common characteristics or categories that the first three words share. What distinguishes the fourth word?

  2. Q2.easy

    In a certain code, 'APPLE' is written as 'BQQMF'. How would 'GRAPE' be written in that code?
    1. A)HSBQG
    2. B)HSBQF
    3. C)HRBQG
    4. D)HRBQF
    Show answer

    Answer: HSBQF

    Hint: Analyze the change in each letter from 'APPLE' to 'BQQMF'. Is there a consistent shift or pattern for each letter?

  3. Q3.easy

    What will come in place of the question mark (?) in the following series?
    3, 7, 15, 31, 63, ?
    1. A)125
    2. B)127
    3. C)129
    4. D)131
    Show answer

    Answer: 127

    Hint: Look for the relationship between consecutive terms. Is there a multiplication or addition pattern that changes with each step?

  4. Q4.medium

    Find the odd one out: 121, 289, 361, 529, 676.
    1. A)121
    2. B)289
    3. C)361
    4. D)676
    Show answer

    Answer: 676

    Hint: All numbers are perfect squares. Examine the properties of their square roots.

  5. Q5.medium

    In a certain code, 'MATHEMATICS' is coded as 'AMHTMEACIST'. How would 'OLYMPIAD' be coded in the same language?
    1. A)MYLOIPDA
    2. B)LOIYPMDA
    3. C)LOMYIPDA
    4. D)PIMYOLAD
    Show answer

    Answer: LOMYIPDA

    Hint: Observe the transformation in blocks of two letters and then look for a consistent rule for any remaining letters or specific letter changes.

  6. Q6.medium

    Find the missing term in the series: 3, 7, 16, 35, ?, 153.
    1. A)69
    2. B)72
    3. C)74
    4. D)78
    Show answer

    Answer: 74

    Hint: Look for a combination of multiplication and addition that links consecutive terms, where the additive part also follows a pattern.

  7. Q7.hard

    Find the missing number in the series: 3, 7, 18, 44, 95, ?
    1. A)176
    2. B)180
    3. C)196
    4. D)204
    Show answer

    Answer: 196

    Hint: Look for a pattern involving both addition and multiplication, possibly with increasing factors.

  8. Q8.hard

    Find the missing number in the series: 3, 7, 18, 44, 95, ?
    1. A)176
    2. B)180
    3. C)196
    4. D)204
    Show answer

    Answer: 196

    Hint: Consider the relationship as (previous term × 2) + an increasing sequence of numbers.

  9. Q9.hard

    Find the missing number in the series: 3, 7, 18, 44, 95, ?
    1. A)176
    2. B)180
    3. C)196
    4. D)204
    Show answer

    Answer: 196

    Hint: Look for a pattern where each term is derived from the previous one using multiplication and an increasing addition sequence.

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.