This series of 'overlapping' ratios can be dealt with by TESTing VALUES.
We're given the following ratios to work with:
We're asked for the ratio of P:H
Based on the given ratios, we know that E is a multiple of BOTH 3 and 5, so let's TEST E = 15....
E = 15
S = 6
P = 4.5
H = 25
We now have a "grand ratio" that involves all 4 variables. Since we cannot have "half" a Psychology teacher, we can multiply each of these values by 2....this gives us....
E = 30
S = 12
P = 9
H = 50
The question asks for the ratio of the number of Psychology majors to the number of History majors...
GMAT assassins aren't born, they're made,
EMPOWERgmat GMAT Club Page, Study Plans, & Discounts