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About Logical Reasoning — Class 10 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 10 mathematics syllabus (chapter: Module 13). On this page you can practice 51 questions across three difficulty levels — 20 easy, 20 medium, and 11 hard — each with a visual step-by-step solution, plus a timed 28-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Logical Reasoning — solved examples for Class 10 Olympiad

Example 1easy

Identify the relationship between the first pair and apply it to the second pair: 12 : 156 :: 15 : ?
  1. A)180
  2. B)210
  3. C)240
  4. D)255

Step-by-step solution

  1. Analyze the first pair: 12 : 156. We observe that 156 = 12 × 13.
  2. The pattern is 'n : n × (n + 1)'. Here, for the first number 'n', the second number is 'n' multiplied by 'n+1'.
  3. Apply this pattern to the second pair. For 15, 'n' is 15.
  4. So, the missing number is 15 × (15 + 1) = 15 × 16 = 240.

Answer: 240

Example 2medium

Identify the relationship: PRIME : IRREDUCIBLE :: COMPOSITE : ?
  1. A)DIVISIBLE
  2. B)FACTORABLE
  3. C)REDUCIBLE
  4. D)NON-PRIME

Step-by-step solution

  1. A prime number is defined as an integer greater than 1 that has no positive divisors other than 1 and itself, making it 'irreducible' in the context of integer factorization.
  2. A composite number is an integer greater than 1 that is not prime, meaning it can be formed by multiplying two smaller positive integers. Therefore, it can be 'reduced' or broken down into its prime factors.
  3. The analogy reflects this fundamental mathematical property: Prime numbers are irreducible, while composite numbers are reducible.

Answer: REDUCIBLE

Example 3hard

The sequence 2, 5, 13, 34, 89, ? follows a unique mathematical pattern. Identify the next term in this sequence.
  1. A)144
  2. B)233
  3. C)235
  4. D)289

Step-by-step solution

  1. The given sequence is 2, 5, 13, 34, 89.
  2. Let's recall the Fibonacci sequence: F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_10=55, F_11=89, F_12=144, F_13=233.
  3. Upon inspection, the given sequence consists of alternate Fibonacci numbers, starting from F_3: F_3=2, F_5=5, F_7=13, F_9=34, F_11=89.
  4. Following this pattern, the next term must be F_13, which is 233.

Answer: 233

Practice questions on Logical Reasoning

  1. Q1.easy

    Choose the word that is different from the rest:
    1. A)Cube
    2. B)Sphere
    3. C)Cylinder
    4. D)Polygon
    Show answer

    Answer: Polygon

    Hint: Consider the fundamental geometric properties of each shape, specifically their dimensionality.

  2. Q2.easy

    In a certain code language, if 'APPLE' is coded as 55 and 'GRAPE' is coded as 52, how would 'ORANGE' be coded?
    1. A)62
    2. B)66
    3. C)70
    4. D)72
    Show answer

    Answer: 66

    Hint: Try assigning numerical values to each letter based on its alphabetical position (A=1, B=2, ... Z=26) and look for a simple arithmetic operation involving the sum of these values and the number of letters.

  3. Q3.easy

    What will come in place of the question mark (?) in the following number series: 1, 4, 13, 40, 121, ?
    1. A)364
    2. B)361
    3. C)358
    4. D)370
    Show answer

    Answer: 364

    Hint: Examine the differences between consecutive terms. If the first differences don't reveal a clear pattern, look at the differences of the differences, or consider multiplication/addition patterns.

  4. Q4.medium

    Find the odd one out from the following list of numbers: 121, 289, 441, 625, 841, 1024.
    1. A)121
    2. B)441
    3. C)625
    4. D)1024
    Show answer

    Answer: 441

    Hint: All numbers are perfect squares. Examine the properties of their respective square roots to find the unique characteristic.

  5. Q5.medium

    If 'CONSTELLATION' is coded as 'TELLATIONCONS', how would 'INNOVATION' be coded using the same logic?
    1. A)VATIONINNO
    2. B)NOVATIONIN
    3. C)INNOVATION
    4. D)OINNINNOVA
    Show answer

    Answer: VATIONINNO

    Hint: Analyze how the word 'CONSTELLATION' is split into two parts and then rearranged to form the coded word.

  6. Q6.medium

    What is the next term in the series: 0, 6, 24, 60, 120, ?
    1. A)180
    2. B)210
    3. C)240
    4. D)260
    Show answer

    Answer: 210

    Hint: Consider the relationship of each term to a perfect cube or a number multiplied by its consecutive integers.

  7. Q7.hard

    In a peculiar coding system, 'PROBLEM' is coded as 'QPRXQYT'. Using the same logic, how would 'SOLUTION' be coded?
    1. A)TNHVOMW
    2. B)RKVWLYQ
    3. C)TNHXPMV
    4. D)RKVXLXW
    Show answer

    Answer: TNHVOMW

    Hint: Analyze the shift for each letter in 'PROBLEM' based on its position. The shift might follow a patterned increment or decrement.

  8. Q8.hard

    If 'MATRIX' is coded as 'NBWSIX', then 'VERBAL' is coded as:
    1. A)WFYCBM
    2. B)WFYCBN
    3. C)XGZCBO
    4. D)XGYCBP
    Show answer

    Answer: WFYCBN

    Hint: Examine the shift for each letter individually. The shift might not be uniform but could depend on the letter's position or value in a non-obvious way.

  9. Q9.hard

    The sequence of figures progresses by specific transformation rules. Figure 1 shows a square with a small dot at its top-left vertex. Figure 2 shows a pentagon with a small dot at the midpoint of its top-most edge. Figure 3 shows a hexagon with a small dot at its top-right vertex. Figure 4 shows a heptagon with a small dot at the midpoint of its right-most edge. Which of the following describes Figure 5?
    1. A)An octagon with a small dot at its bottom-right vertex.
    2. B)An octagon with a small dot at the midpoint of its bottom-right edge.
    3. C)A nonagon with a small dot at its bottom-right vertex.
    4. D)A nonagon with a small dot at the midpoint of its bottom-right edge.
    Show answer

    Answer: An octagon with a small dot at its bottom-right vertex.

    Hint: Observe two distinct patterns: how the outer shape changes (number of sides) and how the dot moves around the perimeter.

These are 9 of the 51 questions available for Logical Reasoning. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.