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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed is consistent?
X=9, Y=8
X=27, Y=22
X=27, Y=64
X=81, Y=16
X=9, Y=8
Quick Trick: Identify the cubic relationship between numbers; recognize that 729 is 9 cubed and 512 is 8 cubed.
Identify the cubic relationship between numbers; recognize that 729 is 9 cubed and 512 is 8 cubed.
Analyze the existing pairs
Observe the relationship X: 729 and 512: Y. We know that 9 raised to the power of 3 (999) equals 729, and 8 raised to the power of 3 (888) equals 512.
Apply logic to the missing variables
If the pattern follows the format (n┬│) where the base is n, then X must be 9 to result in 729, and Y must be 8 because 512 is 8 cubed.
B: 27 cubed is 19683 and 22 cubed is 10648, which does not match the provided numbers. C: 27 cubed and 64 cubed do not result in 729 and 512. D: 81 cubed and 16 cubed far exceed the given values in the analogy.
A is correct because the pattern is defined by the cube of the base number: 9 cubed equals 729 and 8 cubed equals 512.
Always memorize cubes up to 15 and squares up to 30; they frequently appear in number analogy and series questions.