GRE Sample Test 3 Quantitative Reasoning 2

Whenever a question provides multiple ratios with a common element, manipulate the ratios so that the common element has the same value in both ratios. In this case, the common element is teachers, so we should manipulate the ratios so that the number of teachers is the least common multiple of 2 and 5: 10. In the first ratio: students/teachers = $\frac{9}{2}$ = $\frac{45}{10}$
In the second ratio: teachers/administrators = $\frac{5}{3}$ = $\frac{10}{6}$. The ratio of students to teachers to administrators is thus 45:10:6. The number of students must therefore be a multiple of 45. Any choice that is a multiple of 45 is a potential value for the number of students.