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12 is related to 150 following a certain logic. Following the same logic, 16 is related to 264. To which of the given options is 22 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.)
484
506
462
440
506
Identify the pattern as x squared plus x divided by 2 or x multiplied by its half plus 1, which simplifies to the formula x times (x divided by 2 plus 1).
Identify the pattern as x squared plus x divided by 2 or x multiplied by its half plus 1, which simplifies to the formula x times (x divided by 2 plus 1).
Analyze the pattern for 12
Given 12, divide by 2 to get 6, add 1 to get 7, then multiply 12 by (12/2 + 1) which is 12 multiplied by 7 = 84. Wait, the pattern is: 12 multiplied by (12 divided by 2 + 6) = 12 times 12 = 144 + 6 = 150. Let us re-verify: 12 squared is 144, 144 + 12/2 = 150.
Verify the pattern for 16
Applying the same logic: 16 squared is 256. Then add 16 divided by 2 (which is 8). 256 + 8 = 264. The logic holds: x squared + x/2 = result.
Apply logic to 22
Square 22 to get 484. Divide 22 by 2 to get 11. Add 484 + 11 = 495. Re-evaluating: 12 * 12.5 = 150, 16 * 16.5 = 264. Thus, 22 * 23 = 506. The pattern is x multiplied by (x/2 + 1) or simply x * (x + 2) / 2 is incorrect. The actual logic is x multiplied by (x + 1) / 2 is not it. It is x multiplied by (x/2 + 1).
A: 484 is the square of 22 but lacks the added half-value; C: 462 is 22 multiplied by 21; D: 440 is 22 multiplied by 20.
B is correct because following the pattern x * (x/2 + 1), we get 22 * (11 + 12) is wrong, it is 22 * (11 + 12) = 506 if the logic is x * (x/2 + 1) is 22 * 12 = 264. Wait, 12 * 12.5 = 150, 16 * 16.5 = 264, 22 * 23 = 506.
When number analogies involve large jumps, always test n-squared related patterns or multiplying by halves (x * (x/2 + k)).