Number Analogy Patterns for Logical Reasoning

Number Analogy Patterns for Logical Reasoning

Number analogy questions will have a set of two numbers having a particular arithmetic relationship with each other. You have to identify this relationship and apply it to find the missing analogous term of the next set of numbers. 

A big majority of number analogy questions fall into 5 categories and thus can be solved in 5 steps.

Number Analogy


Step 1: Try to see if the relationship between the two numbers is a simple arithmetic operation like addition, subtraction, multiplication or division by another number. Chances are that the operations will either be multiplication or division.

 

Step 2: If the relationship is not that of a single arithmetic operation, check for multiple operations of the form (a*b)+c or other operations of the same fashion.

 

Step 3: If any of the numbers are perfect squares or cubes or are raised to any particular power, the pair of numbers will probably be having a relationship based on exponentiation. Questions from this category will also have the exponentiation function in connection with other arithmetic operations so that the relationship is not directly identifiable. A typical case is when a constant is added to or subtracted from an exponential number.


Step 4: Analogies can also occur in the form of patterns. Try to identify any notable patterns by looking at the nature of each number. For e.g.  42: 56 :: 72: ? is following the pattern a(a+1): (a+1)(a+2)

 

Step 5: If the analogies are in the form of alphabets, determine the ordinal status of each alphabet and identify the numerical relationship so implied. For e.g.  C: F :: D: ? follows the relationship where the ordinal status of the first alphabet is multiplied by 2 to obtain the second alphabet.



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Solved Examples

Q.1. Choose the best alternative.

26 : 5 : : 65 : ?

  1. 5
  2. 6
  3. 7
  4. 8

Solution: The relationship is (x² + 1) : x.

Hence the answer will be 8.


Q.2. Choose the best alternative.

7 : 56 : : 9 : ?

  1. 63
  2. 81
  3. 90
  4. 99


Solution: The relationship is x : x (x + 1).

Hence the answer will be 90.


Q.3. Choose the best alternative.

14 : 9 : : 26 : ?

  1. 12
  2. 13
  3. 14
  4. 15


Solution: The relationship is (2x – 4) : x.

Hence the answer will be 15.

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Q.4. Choose the best alternative.

42 : 56 : : 110 : ?

  1. 132
  2. 134
  3. 136
  4. 138


Solution: Clearly, 42 = 7 × 6 and 56 = 7 × (6 + 2). Similarly, 110 = 11 × 10. So, required number =11× (10 + 2) = 11 × 12 = 132.



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Q.5. Choose the best alternative.

149 : 238 : : 159 : ?

  1. 248
  2. 251
  3. 270
  4. 260


Solution: The relationship is x : (x + 89).

Hence the answer will be 248.


Q.6. Choose the best alternative.

68 : 130 : : ? : 350

  1. 232
  2. 222
  3. 242
  4. 252


Solution: Clearly, 68 = 4³ + 4; 130 = 5³ + 5; 350 = 7³ + 7. So, missing number = 6³ + 6 = 216 + 6 = 222.


Q.7. Choose the best alternative.

42 : 56 ; ; 72 : ?

  1. 81
  2. 90
  3. 92
  4. 96


Solution: Clearly, 42 = 6 × 7; 56 = 7 × 8; 72 = 8 × 9. So, missing number = 9 × 10 = 90.


Q.8. Choose the best alternative.

5 : 36 : : 6 : ?

  1. 44
  2. 49
  3. 48
  4. 46


Solution: The relationship is x : ( x + 1)².

Hence the answer will be 49.



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Q.9. Choose the best alternative.

583 : 293 : : 488 : ?

  1. 222
  2. 378
  3. 392
  4. 300


Solution: Sum of digits of the first number is 2 more than the sum of digits of second number.

Hence the answer will be 378.


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Number Analogy Patterns | Concepts, Solved Examples

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