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.
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.
Q.1. Choose the best alternative.
26 : 5 : : 65 : ?
Solution: The relationship is (x² + 1) : x.
Hence the answer will be 8.
Q.2. Choose the best alternative.
7 : 56 : : 9 : ?
Solution: The relationship is x : x (x + 1).
Hence the answer will be 90.
Q.3. Choose the best alternative.
14 : 9 : : 26 : ?
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 : ?
Solution: Clearly, 42 = 7 × 6 and 56 = 7 × (6 + 2). Similarly, 110 = 11 × 10. So, required number =11× (10 + 2) = 11 × 12 = 132.
Q.5. Choose the best alternative.
149 : 238 : : 159 : ?
Solution: The relationship is x : (x + 89).
Hence the answer will be 248.
Q.6. Choose the best alternative.
68 : 130 : : ? : 350
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 : ?
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 : ?
Solution: The relationship is x : ( x + 1)².
Hence the answer will be 49.
Q.9. Choose the best alternative.
583 : 293 : : 488 : ?
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.