emmak wrote:
On planet Simplon, each year has 12 months, each of which consists of exactly 30 days. If Simplon experiences a political scandal every 2/3 of a year, an environmental crisis every 1/6 of a year, and a terrible movie opening every 1/36 of a year, then what is the ratio of the number of political scandals to the number of environmental crises to the number of terrible movie openings experienced over a five year period on Simplon? (Assume that all three events happen 2/3, 1/6, and 1/36 of a year after the beginning of the first year, and recur at their respective rates after that.)
A. 24 : 4 : 1
B. 1 : 4 : 24
C. 4 : 15 : 90
D. 1 : 6 : 36
E. 3 : 10 : 72
We can think of this as a few different ratios, Political:Environmental, Political:Movie, Environmental:Movie.
Let's look at the first one, P:E. Every 2/3 of a year is the same as every 4/6 of a year. So P is every 4/6 of a year and E is every 1/6 of a year. Which happens more often? E. And at what ratio? 1:4. So, we need the first:second numbers in our ratio to be 1:4 or some multiple thereof. Only answer choice B fits.
Answer choice B.
What if there had been more than one that worked for the above? Let's look at E:M. Every 1/6 of a year is the same as every 6/36 of a year. So E is every 6/36 of a year and M is every 1/36 of a year? Which happens more often? M. And at what ratio? 1:6. So, we need the second:third numbers in our ratio to be 1:6 or some multiple thereof. B, C, and D all work.