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7 : 343 :: 9 : ?
729
512
81
656
729
Identify the base relationship: the first number is raised to the power of three (n cubed) to produce the second number.
Identify the base relationship: the first number is raised to the power of three (n cubed) to produce the second number.
Analyze the first pair
The relationship between 7 and 343 is that 343 is the cube of 7. Mathematically, 7 power 3 = 7 * 7 * 7 = 343.
Apply the rule to the second pair
Apply the same cubing logic to the number 9. Calculate 9 power 3 = 9 * 9 * 9 = 729.
B: 512 is 8 cubed, which does not match the input 9. C: 81 is 9 squared, not 9 cubed. D: 656 is not a perfect cube of an integer related to this pattern.
A is correct because the logic follows the n to n cubed pattern, where 9 raised to the power of 3 results in 729.
For number analogy questions, always test basic operations like squares, cubes, and prime number sequences first before moving to complex multi-step arithmetic.
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