Scientists have determined that Radon - a colorless,

Hi,

Please find below the official solution:

Understanding the Argument

Conclusion
Earth’s age can be estimated by:
• determining the increase in Progeny in earth’s atmosphere over the last 200 years and
• using it to determine how many years it would have taken to reach current levels of Progeny

Premises
1. Radon gas is unstable because of its radioactive nature and continuously decays into Progeny
2. There was no Progeny at the time of earth’s formation

Prethinking

What is the fundamental assumption?

While making his claim, the author assumes that the rate of change of Progeny over the past 200 years is representative of the rate of change of Progeny over the course of history of earth. If this is not the case, i.e. if the rate of change today is much lower or much higher than what it used to be in the past, then the estimates would either be too high or too low.
You may go to the analysis of answer choices if the above makes sense to you. Otherwise, read below if you need more explanation.

Detailed description of how to Prethink

Prethinking in the given question is extremely difficulty unless one has a basic understanding of data representativeness, which basically means that if a sample data is used to make predictions about a population, then the sample data must be representative of the population data. (fundamental assumption)

Since this is pretty technical definition, let’s take an example to understand this. At the end of this example, we will provide a weaken question where the same principle has been used with a twist in a weaken problem.

Suppose you are given a task to estimate the population of a city. Suppose the city has 100 residential blocks. One way to find out the population can be to go to each and every block and count the number of people in each of the blocks and then totaling them to find the total population of the city.

Another way, and a much easier way is estimate the population rather than calculating the same. To do the same you go to, say, 4 residential blocks and find out their populations and calculate the sum of populations in these residential blocks.
Then, the total population of the city can be estimated by multiplying 25 (i.e. 100/4) with the sum of population in these 4 residential blocks.

Do you think this method will work? What if you chose the 4 residential blocks which happen to be the most populous residential blocks in the city? Would you get a correct estimate of the population in such a case?

The answer is No. You would get an estimate which is much higher than the actual population. Similarly, if you chose the least four populous residential blocks, you would get an estimate which is much below the actual population.

Therefore, to get a correct estimate of the population of the city, you must select 4 residential blocks which have near average populations of all the residential blocks. And if you choose residential blocks in such a way, your sample data (i.e. 4 residential blocks) would be a correct representation of the population and the sample can be called as representative of the population.

Now, let’s apply the same knowledge in the given question. If we are using the increase in the amount of Progeny in the last 200 years to estimate the Earth’s age, then that increase should be representative of the increase that happens every 200 years. This is the assumption required. If the increase in Progeny in the last 200 years is significantly different from such increases in the past, then we would have an incorrect estimate. Therefore, one thing we need to evaluate is whether the increase in Progeny in the last 200 years is representative of such increases since the beginning of the earth.

(A weaken question which uses the same understanding: gasoline-cars-in-papula-country-147427.html)

Analysis of Answer Choices

A. Whether the rate of decay of Radon into Progeny is different during day time and night time? – This is irrelevant. Even if the rates are different during day time from night time, it doesn’t impact the estimate. Incorrect.

B. Whether Progeny is stable or gets converted into some other gas at constant rate? – There are two cases to consider in this option statement:
i. Progeny is stable: In this case, the estimate should work perfectly fine.
ii. Progeny gets converted into some other gas at constant rate –
Since this conversion happens both during the last 200 years and the time since the formation of earth, it doesn’t distorts the estimate. This is because such constant conversion impact the increase in gas in the last 200 years in the same proportion as the increase in gas in the time since the formation of earth. Thus, an estimate of the earth’s age, which would be calculated as below, will not be affected.
Earth’s Age: Total Amount of Progeny in the atmosphere currently*200/Increase in the amount of Progeny in the atmosphere in the last 200 years
Incorrect.

C. Whether there have been any changes in the atmosphere in the past century that have increased the radioactivity decay level of all gases? – As we discussed in the Pre-thinking stage, if this given option statement is true, last 200 years of data regarding increase in progeny would not be representative of the time since the formation of Earth. Therefore, we need to find out the answer to this question to know whether the data of increase of Progeny in the last 200 years can be used to estimate the Eath’s age. Correct.

D. Whether there are methods, better than the method given, to estimate the earth’s age? – We are not concerned with an answer to this. Incorrect.

E. Whether amount of Radon or Progeny varies from region to region? – Since we considering the earth’s atmosphere as a whole, even if Progeny varies from region to region, it doesn’t impact the estimate because we are taking into account all the regions. Incorrect.

Hope this helps

Thanks,
Chiranjeev