Choose the similar pair for the following: 343 : 6 :: _____ : _____

Solution: Identify the rule that maps the first number to the second number.

• Observation: 343 = 7^3, and 6 = 7 − 1. So the rule is to take the cube root of the first number and subtract 1.

• Apply the rule to each choice: For 512, 512 = 8^3, and 8 − 1 = 7, so 512 : 7 follows the same rule as 343 : 6.

• Check the other choices briefly: 225 = 15^2 (fits a square-root pattern, not the cube-root-minus-one rule); 256 and 196 are not perfect cubes, so they do not produce the integer second values required by the cube-root-minus-one pattern.

Therefore the similar pair is 512 : 7.