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

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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Feb 2013, 02:10, edited 1 time in total.
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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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.)

24 : 4 : 1

1 : 4 : 24

4 : 15 : 90

1 : 6 : 36

3 : 10 : 72


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.
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 18 Apr 2013, 07:49
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?
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 18 Apr 2013, 09:19
Transcendentalist wrote:
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
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 18 Apr 2013, 09:25
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


Total days per year = 12*30=360
For 5 years = 12*30*5=1800

political scandal happens every 2/3 of a year = 2/3 * 360 = 240days
This implies for every 240 days 1 political scandal occurs.
which means for 5yrs or 1800 days, no.of scandals that happen = 1800/240 = 15/2

smilarly environment damage happens every 1/6 of a year = 1/6 * 360 = 60 days
This implies for every 60 days 1 environmental damage occurs.
For 5yrs or 1800 days, no.of environmental damages that occur = 1800/60 = 30

smilarly a terrible movie opening happens every 1/36 of a year = 1/36 * 360 = 10 days
This implies for every 10 days 1 terrible movie opening happens.
For 5yrs or 1800 days, no.of environmental damages that occur = 1800/10 = 180

Answer==> political scandal for 5yrs : Env damages for 5yrs : Terrible movie opening for 5yrs = 1800/240 : 1800/60 : 1800/10

or 15/2 : 30 : 180 = 15 : 60 :360 = 1 : 4 : 24

B
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 18 Apr 2013, 09:31
Zarrolou wrote:
Transcendentalist wrote:
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
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 18 Apr 2013, 12:18
Expert's post
Transcendentalist wrote:
If a scandal occurs every 8 months over a 5 year period exactly 7 scandals would have occurred. So shouldn't the ratio be

7:30:180?


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?
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 19 Apr 2013, 08:12
vinaymimani wrote:
Transcendentalist wrote:
If a scandal occurs every 8 months over a 5 year period exactly 7 scandals would have occurred. So shouldn't the ratio be

7:30:180?


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?
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 19 Apr 2013, 08:28
Expert's post
Transcendentalist wrote:
vinaymimani wrote:
Transcendentalist wrote:
If a scandal occurs every 8 months over a 5 year period exactly 7 scandals would have occurred. So shouldn't the ratio be

7:30:180?


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.
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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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
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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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


Detouring briefly from the tangent questions, a nice shortcut to solve this original questionquickly is to think of the numbers in months. You then see that political scandals happen every 8 months and environmental crises happen every 2 months, so the ratio must be 1:4 (or a multiple thereof) regardless of the terrible movie openings (Die Hard 5 anyone??). The only answer choice with the 1:4 ratio is B. No need to go any further. On different questions if you can eliminate answer choices based on two of the three entries, then you don't have to try mentally juggling the three.

Hope this helps!
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 30 May 2014, 09:30
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
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Re: On planet Simplon, each year has 12 months, each of which [#permalink]

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On planet Simplon, each year has 12 months, each of which [#permalink]

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New post 13 Oct 2015, 21:13
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.
On planet Simplon, each year has 12 months, each of which   [#permalink] 13 Oct 2015, 21:13
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