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Complete the analogy: 12 : 144 :: 15 : ?
225
255
180
150
225
The relationship is a simple square of the first number; square the given number on the right side of the colon to find the answer.
The relationship is a simple square of the first number; square the given number on the right side of the colon to find the answer.
Analyze the relationship
Observe the first pair: 12: 144. Mathematically, 144 is the square of 12 (12 * 12 = 144).
Apply the rule
Apply the same logic to the second pair: 15:?. Square the number 15 (15 * 15 = 225).
B: 255 is incorrect because it is not a perfect square and does not follow the n:n² pattern. C: 180 is incorrect as it results from 15 * 12, not 15 * 15. D: 150 is incorrect because it is 15 * 10, lacking logical consistency with the first pair.
A is correct because the pattern follows the rule n : n squared, where 15 squared equals 225.
For number analogies, always check for squares, cubes, and prime numbers first, as these are the most common relationships found in competitive exams.
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