1. **State the problem:** Gillian has three test scores. The first is 90, the second is 75, and the third is unknown. We want to find the lowest score on the third test so that the average of all three tests is 85. 2. **Formula for average:** The average of three numbers $a$, $b$, and $c$ is given by $$\text{Average} = \frac{a + b + c}{3}$$ 3. **Set up the equation:** Let the third test score be $x$. We want $$\frac{90 + 75 + x}{3} = 85$$ 4. **Multiply both sides by 3 to clear the denominator:** $$90 + 75 + x = 3 \times 85$$ $$90 + 75 + x = 255$$ 5. **Add the known scores:** $$165 + x = 255$$ 6. **Isolate $x$ by subtracting 165 from both sides:** $$\cancel{165} + x - \cancel{165} = 255 - 165$$ $$x = 90$$ 7. **Interpretation:** Gillian needs to score at least 90 on her third test to have an overall average of 85. **Final answer:** $\boxed{90}$