12 is related to 235 by certain logic. Following the same logic, 14 is related to 287. To which of the following is 18 related, following the same logic? (Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)

Question

Accepted Answer

Step 1: Analyze the given pairs: 12 → 235 and 14 → 287.
Step 2: Check if the output numbers relate to the input number by some arithmetic operation on the whole number.
Step 3: For 12 and 235:
- 12 squared = 144
- 12 cubed = 1728
- Sum of squares and cubes or any direct arithmetic does not give 235.
Step 4: Check if the output number is formed by adding or subtracting some function of the input number:
- 12 × 19.58 ≈ 235 (approximate, but not exact)
Step 5: Try to find a pattern in digits:
- 235 is close to 12 × 19.58
- 287 is close to 14 × 20.5
Step 6: Check if the output number is formed by concatenating (input number + 1), (input number + 2), (input number + 3) or similar:
- For 12: 2, 3, 5 are digits, but 2,3,5 are not consecutive numbers related to 12.
Step 7: Try sum of digits of output:
- 2+3+5=10
- 1+2=3
- 2+8+7=17
- 1+4=5
No clear relation.
Step 8: Try to check if output number is sum of input number squared and input number plus some constant:
- 12^2=144; 144 + 91=235
- 14^2=196; 196 + 91=287
Step 9: So, the logic is: Output = (Input number)^2 + 91
Step 10: For 18:
- 18^2 = 324
- 324 + 91 = 415
Step 11: Hence, 18 is related to 415.
Therefore, option 2 (415) is correct.

Answer

Answer

Answer