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First of all let's identify the main conclusion of the argument. The main conclusion is that advanced experience and learned propensity for caution possessed by doctors in the 60 and older group make them far more reliable than younger doctors are. Let's check option one by one which is acting as assumption :

(A) The first one is not an assumption since it is comparing error rate between doctors aged less than 30 and 30-35. The main conclusion is talking about 60 and older. Even if we negate this option , the argument still holds.
(B) Not an assumption since if we negate it , it will become doctors aged 60 years and above do make up a meaningfully larger fraction of physicians in Darrenville than doctors between the ages of 30 and 35 do. Still the argument holds.
(C) This is an assumption. If we negate it then it will become Doctors 60 years and above are more likely to perform medical procedures under circumstances that significantly heighten the risk of errors. This will make the argument fall since main conclusion says that higher experience corresponding for 60 and older , higher reliability.
(D) Treating patients comparison is out of assumption and context. Not an assumption.
(E) E is irrelevant. Not an assumption.
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Last year, 10 percent of doctors younger than 30 and 7 percent of doctors between the ages of 30 and 35, practicing in Darrenville, made at least one avoidable error during a medical procedure. On the other hand, only 2 percent of doctors 60 and older made such an error. These findings make it clear that the advanced experience and learned propensity for caution possessed by doctors in the 60 and older group make them far more reliable than younger doctors are.

Which of the following is an assumption on which the argument depends?

(A) The difference between the error rate of doctors under 30 and of those between 30 and 35 can be attributed to the higher level of medical experience possessed by the older doctors.

(B) Doctors 60 years and above do not make up a meaningfully larger fraction of physicians in Darrenville than doctors between the ages of 30 and 35 do.

(C) Doctors 60 years and above are less likely than are doctors 35 and younger to perform medical procedures under circumstances that significantly heighten the risk of errors.

(D) Doctors 60 years and above, on average, do not, treat a considerably lower number of patients per year than doctors 35 and younger do.

(E) For no age bracket is the error rate lower than it is for doctors 60 and older.

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A. Irrelevant since its talking about the difference between the younger doctors where as we to know between old and young
B. Irrelevant group size isnt necessary when percentages are used
C. Irrelevant as this would undermine the argument not an assumption the argument would depend on (basically it says that the lower error rate is due to safer conditions for older doctors, and not their reliability)
D. Relevant as this is the required assumption for the argument because if older doctors treat fewer patients, then they have fewer chance to make mistakes. Their lower error rate would then not demonstrate their greater reliability. Without this statement, the conclusion isnt justified
E. Irrelevant as it does nothing but restate the given statements

D. Doctors 60 years or above, on average do not treat a considerably lower number patients per year than doctors 35 years and younger do
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The argument's necessary assumption is that older doctors (60+) don't see significantly fewer patients than younger doctors.

A Not needed for the conclusion comparing older vs. younger. It's irrelevant.

B Irrelevant because error rates are percertage of doctors in each age group, not total error counts affected by group size.

C If true, that gives an alternate explanation (easier cases) for lower error rate, undermining the argument.

D If they did treat fewer patients, they'd have fewer chances to error, so the lower percentage of doctors with an error might not mean better skill per procedure. The argument ignores this possibility, so must assume it's false, making D the necessary assumption.

E It's irrelevant to why older doctors have lower rates. No need for this to be true for the argument to stand.


The correct answer is D
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Solution:
Option A => The argument holds a correlation between mistakes in percentage vs age. It is irrelevant to the doctors who are 60+. No such assumption required. Eliminate.
Option B => The fraction in Darrenville is not a factor. The percentage of people making mistakes in the group is. Eliminate.
Option C => The circumstances are again a third factor (complexity of medical procedure) which is not required for consideration. Eliminate.
Option D => The number of patients are a good factor to keep in mind. If the doctors reduce the number of patients they treat with age, the number of errors will also go down. So this assumption is required. Correct.
Option E => The other age brackets are not mentioned and hence out of scope. Eliminate.

Correct Answer => D
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When we are comparing different groups on percent, the meaningful argument can be put up only if the total is in comparable figure. Otherwise the comparison is flawed one. So, D is right answer
Bunuel
Last year, 10 percent of doctors younger than 30 and 7 percent of doctors between the ages of 30 and 35, practicing in Darrenville, made at least one avoidable error during a medical procedure. On the other hand, only 2 percent of doctors 60 and older made such an error. These findings make it clear that the advanced experience and learned propensity for caution possessed by doctors in the 60 and older group make them far more reliable than younger doctors are.

Which of the following is an assumption on which the argument depends?

(A) The difference between the error rate of doctors under 30 and of those between 30 and 35 can be attributed to the higher level of medical experience possessed by the older doctors.

(B) Doctors 60 years and above do not make up a meaningfully larger fraction of physicians in Darrenville than doctors between the ages of 30 and 35 do.

(C) Doctors 60 years and above are less likely than are doctors 35 and younger to perform medical procedures under circumstances that significantly heighten the risk of errors.

(D) Doctors 60 years and above, on average, do not, treat a considerably lower number of patients per year than doctors 35 and younger do.

(E) For no age bracket is the error rate lower than it is for doctors 60 and older.

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