13 is related to 119 following a certain logic. Following the same logic, 9 is related to 31. To which of the following is 8 related, following the same logic?

(Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

Question

13 is related to 119 following a certain logic. Following the same logic, 9 is related to 31. To which of the following is 8 related, following the same logic?

(Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

Accepted Answer

Step 1: Analyze the given pairs:
- 13 is related to 119  
- 9 is related to 31

Step 2: Check if the relation involves any arithmetic operation on the whole number:  
- For 13 and 119:
  Check if 13^2 - 13 = 169 - 13 = 156 (No)  
  Check if 13^2 - 30 = 169 - 30 = 139 (No)  
  Check if 13^2 - 50 = 169 - 50 = 119 (Yes)

So, 13^2 - 50 = 119

- For 9 and 31:  
  Check if 9^2 - 50 = 81 - 50 = 31 (Yes)

Step 3: The logic is: Related number = (Original number)^2 - 50
 
Step 4: Apply the same logic for 8:  
  8^2 - 50 = 64 - 50 = 14

Step 5: Among the options, 14 is present and matches the logic.

Therefore, 8 is related to 14 following the same logic.

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