On planet Simplon, each year has 12 months, each of which

So , the political scandal occurs every 8 months, the environmental crisis every 2 months and the terrible movie opening every (1/3) a month. We just have to find out the ratio between
\(5*\frac{12}{8} : 5*\frac{12}{2} : 5*\frac{12}{(1/3)} = \frac{1}{8} : \frac{1}{2} : 3\)

On multiplying across by 8 , 1:4:24

B.

If a scandal occurs every 8 months over a 5 year period exactly 7 scandals would have occurred. So shouldnt the ratio be

7:30:180?

Hi Transcendentalist,

you missed something. \(5years*12months= 60 months\) one scandal every 8 months means \(\frac{60}{8}=7.5\) scandals
.5 is what makes your option wrong.

This should clarify, let me know

How does .5 of a scandal occur?

Lets say there are 1 scandal every 5 months

In one year - 2 scandals will occur
2 years - 4 scandals will occur
3 years - 7 scandals will occur

Lets assume what you said is correct. The ratio is 7:30:180. So now for every 30 environmental crisis, 7 scandals occur. Thus, for 60 crisis, we should have 14 scandals. But if you go by what is given in the problem, we would have 15 scandals. Any guesses?

Nope the ratio holds true only for 5 years. If the period being considered is 10 years, then the ratio changes. I haven't calculated it out but for every change in no of years the ratio changes accordingly. Makes sense?

I can-not in any way imagine how a given ratio can change depending upon the number of years. Say red:blue balls ratio --> 2:3. So are you telling me that for every 1 red ball the ratio should be 1:1.5(and as per your logic by dropping the 0.5 )-->1:1? So for 1 red ball, the ratio is 1:1, for 2 red balls, the ratio is 2:3 and for 4 red balls, the ratio is again 2:3?

The fact that 1.5 balls can't exist is correct. But the fact that ratio can be presented in myriad ways is also correct. So when I say that the ratio of red:blue balls = 2:3 = 1:1.5 --> it is all correct. It is just that the latter ratio is an intermediate value, something which is mathematically correct yet not feasible,physically. The fact that for 10 years , the value 7.5=15/2 when multiplied by 2 gives an integral value is the reason why we have 15 scandals over 10 years, which is not possible for 5 years as it gives a non-integral value(7.5);which is mathematically correct, yet not feasible in the physical world.

Lets just start with a blank slate.. Would you please answer the following problem for me?

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 (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.)

Can you please calculate the ratio of the No of following events over a 5 year period to that over a 10 year period?

1, Political Scandal
2, Environmental Crises
3, Terrible

Actually, we only need to take the ratio of 3/2:6:36 which are the denominators and one will get 1:4:24.

Thus answer is B

I know it's been a while, but I'd like to back up Transcendentalist here. Here's why he's right:

What is the ratio of Mondays to Tuesdays in an 8 day period starting and ending with Monday?
The answer here is not 1:1. Let's look at the sample space:
M T W TH F S S M
We see that 2 Mondays, but only one Tuesday. Therefore the ratio is 2:1.
For 9 days we would see:
M T W TH F S S M T
Making the ratio 1:1 again.

A simple example:
What is the ratio of odds to evens in the range 1-101 inclusive? In 1-100?
I think we can all tell that there are 51 odds and 50 evens in the first part of the question, making the ratio 51:50. In the second part there are 50 of each giving 50:50 or 1:1.

Another analogous problem:
Bob is pushing a boulder up a 100 meter long hill. Every day he pushes it up 20 meters. Then when he rests, it rolls down 11 meters. How many days would it take Bob to push to boulder up to the top of the hill? Answer as an integer, and assume the boulder no longer rolls down once the top of the hill is reached.
Hastily, we would calculate the average rate of 20-11=9 meters per day. 11 x 9 = 99, and that's not quite enough, so the answer must be 12 days (12 x 9 = 108 meters).
Let's go back a step. Before he starts pushing on the beginning of the 10th day, Bob's boulder is at 9 x 9 = 81 meters. Now he pushes the boulder up 20 meters, reaching 101 meters. The answer here is therefore 10 days, not 12.

The point in these three examples is that, depending on the problem, using a constant ratio or rate doesn't work. The ratio changes depending on the period we're looking at.

I guess we needed to take 7.5 as a value.

I thought we can't really take the .5 hence thought it would 7:30:180 and C was the closest option.

I do not think this is a good question even though the source is `Veritas.
I am also not convincing that B is the answer.
It is because in the last year, the first event cannot occur while the other events keep happening.
Also, I am not sure on what day of a year each event will first takes place.

This is not a good question.

Transcendentalist is correct. If a scandal occurs every 8 months over a 5 year period exactly 7 scandals would have occurred. So the ratio should be

7:30:180.

Transcendentalist is correct
the number of scandals that happend during the 5 years period is 7 , not 7.5
c is the closest

Totally agree with Transcendentalist

I consider that this question is not well fundamented and does have a wrong answer. My reason to say that is that question is asking "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"

Over a 5 year period, Simplon's habitants would experience 7 political scandals as it impossible to experience half a political scandal, therefore, the ratio would be 7:30:180.

I think the key is the assumption in the brackets that suggest starting to count the recurrence from time 0. This way we get 7:30:180.

In case the question asked for the ratio over a random 5 year period, the most appropriate answer (the average, I guess) would be B.

Hi Transcendentalist,

I proceeded the same way and I believe yours would have been the correct solution in case it was asked for the first 5 years. However, as the question-asked ratio for any 5 years period, we need to calculate the average, i.e. consider the 7.5 political scandals. Why does it matter? consider another scenario of the second "5-year period" from the beginning. In this 5 years period, we will get to observe 8 political scandals ((there will be 7 & 8 political scandals in alternate 5 years periods, respectively)). Here, 7:30:180 fails... rather, it's 8:30:180 in this case.

Therefore, when we define in general, it makes sense to consider 7.5:30:180, which clarifies that all the alternate 5-year periods will have 8 political scandals.