1. Problem 207: Find the percent increase in the ratio of price per share to earnings per share given price increase $k\%$ and earnings increase $m\%$ with $k>m$. 2. Let original price be $P$ and original earnings be $E$. The original ratio is $\frac{P}{E}$. 3. After increase, new price is $P(1+\frac{k}{100})$ and new earnings is $E(1+\frac{m}{100})$. 4. New ratio is $$\frac{P(1+\frac{k}{100})}{E(1+\frac{m}{100})} = \frac{P}{E} \times \frac{1+\frac{k}{100}}{1+\frac{m}{100}}.$$ 5. The ratio increase factor is $$\frac{1+\frac{k}{100}}{1+\frac{m}{100}} = \frac{100+k}{100+m}.$$ 6. Percent increase in ratio is $$\left(\frac{100+k}{100+m} - 1\right) \times 100 = \frac{100(k-m)}{100+m}.$$ 7. Therefore, the answer is option D: $\frac{100(k-m)}{100+m}\%$. 8. Problem 208: Of 300 subjects, 40% had sweaty palms, 30% vomiting, 75% dizziness; all had at least one effect; 35% had exactly two effects. Find how many had only one effect. 9. Let $A$, $B$, $C$ be sets of subjects with sweaty palms, vomiting, dizziness respectively. 10. Given: $|A|=0.4\times300=120$, $|B|=0.3\times300=90$, $|C|=0.75\times300=225$. 11. Total subjects $N=300$, all had at least one effect, so $$|A \cup B \cup C|=300.$$ 12. Number with exactly two effects is 35% of 300 = 105. 13. Using inclusion-exclusion: $$|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |B \cap C| - |C \cap A| + |A \cap B \cap C|.$$ 14. Let $x$ be number with all three effects. 15. Number with exactly two effects = sum of pairwise intersections minus thrice the triple intersection: $$|A \cap B| + |B \cap C| + |C \cap A| - 3x = 105.$$ 16. Number with exactly one effect = total with effects - exactly two effects - exactly three effects: $$= (|A| + |B| + |C|) - 2(|A \cap B| + |B \cap C| + |C \cap A|) + 3x.$$ 17. Using the union formula and substituting: $$300 = 120 + 90 + 225 - (|A \cap B| + |B \cap C| + |C \cap A|) + x,$$ so $$|A \cap B| + |B \cap C| + |C \cap A| = 435 - 300 + x = 135 + x.$$ 18. From step 15: $$135 + x - 3x = 105 \Rightarrow 135 - 2x = 105 \Rightarrow 2x = 30 \Rightarrow x = 15.$$ 19. Number with exactly one effect: $$= 435 - 2(135 + 15) + 3(15) = 435 - 2(150) + 45 = 435 - 300 + 45 = 180.$$ 20. Answer is option D: 180. 21. Problem 209: Given $m^{-1} = -\frac{1}{3}$, find $m^{-2}$. 22. Recall $m^{-2} = (m^{-1})^2$. 23. Substitute: $$m^{-2} = \left(-\frac{1}{3}\right)^2 = \frac{1}{9}.$$ 24. Answer is option D: $\frac{1}{9}$. 25. Graph problem: Right triangle with vertices A(0,0), B(4,0), C(4,3), right angle at B. 26. Side lengths: AB = 4, BC = 3, hypotenuse AC = $\sqrt{4^2 + 3^2} = 5$. 27. This confirms the triangle is a 3-4-5 right triangle.