When a person uses information he/she has been taught (e.g., choose formulas and problem-solving strategies) to solve problems in a rational way, Sternberg's triarchic theory of intelligence would suggest that person was demonstrating __________ intelligence.

Sternberg developed a theory in which intelligence has to do with how well the person deals with changes in the environment during the course of their life.

According to this theory, intelligence has three components:

Componential: it refers to the usual academic proficiency, it has to do with possessing analytical skills that allow to solve problems in new ways.
Experiential: It is based in creativity and flexibility, it has to do with how well one person performs a task based on how familiar this task is. Once the task is performed many times, experience makes it doable with no effort or a little effort required.
Practical: this one has to do with context, it refers to how the person can adapt himself/herself to the environment and deal with constantly new situations.

In this question, we are asked for which component of intelligence is shown by a person who uses information he/she has been taught to solve problems in a rational way.

We can see that the component that refers to solving problems using analytical skills is the componential one.

Thus, this person would be demonstrating componential intelligence.