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Select the option in which the numbers share the same relationship: 12 : 148 :: 15 : ?
228
230
232
235
230
Look for the relationship n squared plus n plus some constant or n squared plus n times k. In this case, it follows the pattern of x squared plus x.
Look for the relationship n squared plus n plus some constant or n squared plus n times k. In this case, it follows the pattern of x squared plus x.
Analyze the first pair (12 : 148)
If we square the first number: 12 squared is 144. Then add 4 to 144, we get 148. So the logic is x squared plus 4.
Apply logic to the second pair (15 : ?)
Apply the same logic: 15 squared equals 225. Then add 4 to 225, which gives 229. Since 229 is not an option, we re-evaluate.
Alternative pattern logic
Let us check: 12 multiplied by 12 equals 144, plus 12 divided by 3 (which is 4) equals 148. Applying this to 15: 15 multiplied by 15 is 225, plus 15 divided by 3 (which is 5) equals 230.
A: 228 is incorrect as it does not satisfy the x squared plus x/3 pattern. C: 232 is incorrect as it deviates from the derived formula result of 230. D: 235 is incorrect as it does not follow the established mathematical progression.
B is correct because the pattern follows (x * x) + (x / 3), where 12 * 12 + 12/3 = 148 and 15 * 15 + 15/3 = 230.
When a simple square-based pattern fails, check for relations involving division or multiplication of the base number itself to adjust the result.
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