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carcass
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Option E says that we will not be able to know how much atmospheric radiation is emmitted at a place until we measure it and clearly it can not be inferred from the QS,the question stem only talks about atmospheric radiation as an input to make the output truly random and not predictable,it does not talk anything about measurement of it.so clearly it can't be inferred,if OA was not given anywhere then they would have got E as an answer.
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Computer programs exist that attempt to generate random numbers, but no such program can fully replicate a truly random selection. Computer programs are, by definition, a set of instructions that use an input to generate an output. If both the input and the algorithm are known, the result is fully predictable. Even the best random number generation programs can only be called pseudo-random because the input itself is generated by the program. As a result, a pattern will emerge within the results, even if the program is sophisticated enough to make the pattern very complicated, and that pattern can be used to predict future results. True random number generation often depends on measurement of an unpredictable physical phenomenon, such as weather patterns or atmospheric radiation, and using that measurement as an input to generate a result.

The passage provides information sufficient to infer each of the following statements EXCEPT:

A The outputs of random number generators that provide their own input could, with enough information about past results, eventually be predicted.
B If a person knew both the algorithm that a corporation used to generate a truly random number and the atmospheric measurements that served as the input, the person would be able to generate the same output obtained by the corporation.
C With a sufficiently large table of the results of a pseudo-random number generator over time, it would be possible to derive the input and algorithm used to generate those results.
D The integrity of applications for which the unpredictability of the result is vital, such as lotteries or data encryption, can be best preserved by using a method of random number generation that is truly random.
E It is impossible to know the exact amount of atmospheric radiation emitted at a particular location and time until after a measurement is taken.

The question nowhere talks about what requires use of truly random number generation. How can we derive D from the question then?
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Pseudo-random Generators: Outputs are based on a known algorithm and input, making them predictable if these are known.
True Random Generators: Depend on physical phenomena like atmospheric radiation, which are described as unpredictable.
The passage emphasizes unpredictability but does not explicitly state that atmospheric radiation is impossible to know before measurement.
Option Analysis
E. It is impossible to know the exact amount of atmospheric radiation emitted at a particular location and time until after a measurement is taken.
The passage describes atmospheric radiation as an unpredictable phenomenon used for true random generation. While this implies difficulty in predicting radiation levels, it does not explicitly state that it is impossible to know the exact amount before measurement.
However, unpredictability of radiation is inherent in the concept of true random generation, making this a reasonable inference from the passage.
C. With a sufficiently large table of the results of a pseudo-random number generator over time, it would be possible to derive the input and algorithm used to generate those results.
The passage states that patterns emerge in pseudo-random outputs, but it does not go so far as to say that these patterns can definitively reveal the input and algorithm.
Reverse-engineering a pseudo-random generator requires more than just observing patterns; it depends on additional factors not discussed in the passage, such as computational techniques or knowledge of the program's structure.
This claim goes beyond what is supported by the passage and cannot be inferred directly.
Why Not E?
E is a stronger claim than what the passage explicitly states, but it aligns with the concept of true randomness and unpredictability. Atmospheric radiation is described as unpredictable, which supports the idea that it cannot be precisely known without measurement.
The passage's discussion of unpredictability makes E more reasonable than C, which introduces a claim not addressed in the passage.
Conclusion
The correct answer is C because the passage does not provide sufficient evidence to conclude that the input and algorithm of a pseudo-random generator can be derived solely from observing its outputs. E is supported by the passage's description of atmospheric radiation as an unpredictable phenomenon.
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