In data sufficiency problems, when is a variable considered isolated?

A variable is considered isolated when it can be expressed independently from other variables or constants in an equation. This means that the variable can be solved for without needing to compute the values of others. In the context of data sufficiency questions, an isolated variable is one that does not rely on knowing the values of other variables to determine its own value.

In the case of the correct choice, it highlights that a variable can be surrounded by other numbers yet still not require specific solving. This indicates that, through given equations or expressions, the variable can stand alone in the solution process. This independence is crucial in data sufficiency problems where the goal is often to determine if sufficient information is provided to solve for the variable in question.

The context of the other options does not align as effectively with the concept of isolation. A variable being the only number present does not ensure it is isolated, as isolation pertains to its independence with respect to solving. Expressing a variable as a ratio could involve dependencies on other variables, which does not satisfy the isolation condition. Lastly, a variable appearing outside the equation does not contribute to the definition of isolation, as it might not participate in solving the equation even if it is not directly linked to the values of other variables.