$10$% of all aliens are capable of intelligent thought and have more than $3$ arms, and $75$ % of aliens with $3$ arms or less are capable of intelligent thought. If $40$% of all aliens are capable of intelligent thought, what percent of aliens have more than $3$ arms?

Since all the numbers in this problem are given in percentages, assign a grand total of $100$ aliens. You know that $10$% of all aliens are capable of intelligent thought and have more than $3$ arms. You also know that $75$% of aliens with $3$ arms or less are capable of intelligent thought. It does not say that $75$% of all aliens are capable of intelligent thought. Therefore, assign the variable x to represent the percentage of aliens with three arms or less. Then, the percentage of aliens with three arms or less who are capable of intelligent thought can be represented by $0.75$ x. Since you know that $40$% of all aliens are capable of intelligent thought, you can write the equation $10+0.75x=40$, or $0.75x=30$. Solve for $x:x=40$. Therefore, $40$% of the aliens have three arms or less, and $60$% of aliens have more than three arms.

Thought No Thought Total

Total $40$ $100$