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Very good question indeed! Though other options do not make sense or can be easily eliminated, the answer choice is subtle.
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Researchers announced recently that over the past 25 years the incidence of skin cancer caused by exposure to harmful rays from the sun has continued to grow in spite of the increasingly widespread use of sunscreens. This shows that using sunscreen is unlikely to reduce a person’s risk of developing such skin cancer.

Which one of the following, if true, most weakens the argument?

(A) Most people who purchase a sunscreen product will not purchase the most expensive brand available.
(B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.
(C) The development of sunscreens by pharmaceutical companies was based upon research conducted by dermatologists.
(D) People who know that they are especially susceptible to skin cancer are generally disinclined to spend a large amount of time in the sun.
(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.

Source: LSAT


B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.

This means that people might get effected way before using sunscreen in the first place.
And later when they grow old,having said that they are now using sunscreen,they get skin cancer
Perfect Option
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Researchers announced recently that over the past 25 years the incidence of skin cancer caused by exposure to harmful rays from the sun has continued to grow in spite of the increasingly widespread use of sunscreens. This shows that using sunscreen is unlikely to reduce a person’s risk of developing such skin cancer.

Which one of the following, if true, most weakens the argument?

(A) Most people who purchase a sunscreen product will not purchase the most expensive brand available.
(B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.
(C) The development of sunscreens by pharmaceutical companies was based upon research conducted by dermatologists.
(D) People who know that they are especially susceptible to skin cancer are generally disinclined to spend a large amount of time in the sun.
(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.

Source: LSAT

The problem with E is : There is a huge gap between belief of a person developing a cancer vs actually developing one. If it would have been an experiment of some sort then the psychological effect comes into play. Otherwise that's a huge assumption.

Option B does not directly weaken the usage of sunscreen but instead gives us a different argument. It tells us that skin cancer generally develops among very old people as a result of sunburns experienced when very young. It gives us a reason to believe that may be sunscreen has got nothing to do with skin cancer.
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The argument is that sunscreens are unlikely to reduce the risk of skin cancer. The question asks us to weaken this argument.

The OA -B is strengthening the argument by giving a reason why sunscreen doesn't work. How is B correct?

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Can you explain why E option choice is incorrect? Does it not weaken the conclusion that people who believe that they develop cancer are the ones who are using Sunscreen. So, they anyway are going to get cancer and hence the sunscreen use will not be effective to this set of people.
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Akela
Researchers announced recently that over the past 25 years the incidence of skin cancer caused by exposure to harmful rays from the sun has continued to grow in spite of the increasingly widespread use of sunscreens. This shows that using sunscreen is unlikely to reduce a person’s risk of developing such skin cancer.

Which one of the following, if true, most weakens the argument?

(A) Most people who purchase a sunscreen product will not purchase the most expensive brand available.
(B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.
(C) The development of sunscreens by pharmaceutical companies was based upon research conducted by dermatologists.
(D) People who know that they are especially susceptible to skin cancer are generally disinclined to spend a large amount of time in the sun.
(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.

Source: LSAT

In last 25 years, incidence of skin cancer has continued to grow inspite of more and more use of sunscreen.

Conclusion: Sunscreen is unlikely to reduce a person’s risk of developing such skin cancer.

What will weaken this argument? Something that tells us that the incidence is increasing because of some other factor or that sunscreen does reduce the overall incidence.

(A) Most people who purchase a sunscreen product will not purchase the most expensive brand available.
Irrelevant

(B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.
Correct. The conclusion is based on a 25 year study. But if skin cancer develops among the very old (say 80-90 yr olds) because of sun exposure when they were very young (say 2-10 yrs old), then the sunscreen use of the last 25 years is irrelevant for them. They will develop skin cancer. In the next 50 years, we are likely to see a decrease in the incidence because the very young in the last last 25 years are being protected. So when they grow old, they are likely to be better protected against the disease.
This option tells us that the research numbers of 25 years don't mean anything for skin cancer incidence.

(C) The development of sunscreens by pharmaceutical companies was based upon research conducted by dermatologists.
Irrelevant

(D) People who know that they are especially susceptible to skin cancer are generally disinclined to spend a large amount of time in the sun.
Irrelevant.

(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.
If the most susceptible ones use sunscreen regularly, then we should see a decrease in the number of skin cancer cases. Since the number of cases are increasing, it seems that sunscreen is useless. If anything, this option strengthens the conclusion, not weaken it.

Answer (B)

In E option - I have doubt in E option. Drawing an Analogy before stating my doubt
Example - People who drink soda have higher incidence of alzheimer's disease.
But can we conclude that soda is causing alzheimer's disease?

Not really. Because 1) What if there's some other factor that is causing Alzheimer's disease. For example People mix soda with alcohol and it is the alcohol that is causing Alzheimer's disease. So, even if people stop drinking Soda, they will still have higher incidence of alzheimer's disease.
OR 2) People were supposed to have alzheimer's disease because of some cells/body reactions which caused them to drink more Soda. So. it is not Soda that is causing them alzheimer's disease.

Similarly in E option what if people (who applied sunscreen) already usually develops skin cancer and hence sunscreen effectiveness cannot be judged through this.
This is similar to the 2) explanation given above.

Can you please correct my understanding here? Looking forward to your analysis

Thanks
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Can you explain why E option choice is incorrect? Does it not weaken the conclusion that people who believe that they develop cancer are the ones who are using Sunscreen. So, they anyway are going to get cancer and hence the sunscreen use will not be effective to this set of people.
The author thinks that "using sunscreen is unlikely to reduce a person’s risk of developing [skin cancer caused by exposure to harmful rays from the sun]."

The author believes this because "over the past 25 years the incidence of skin cancer caused by exposure to harmful rays from the sun has continued to grow in spite of the increasingly widespread use of sunscreens."

So how does (E) stack up? Does it point to sunscreen being helpful, harmful, or neutral?
Quote:
(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.
If people who are at risk for skin cancer wear sunscreen most regularly, and yet the incidence of skin cancer has increased despite increased use of sunscreen, then it doesn't seem like the sunscreen is really helping these people to reduce the risk of sunscreen.

In other words, certain people are more likely to get cancer -- so these are EXACTLY the folks who should take precautions so that they don't end up ACTUALLY getting cancer. And sure enough, these people are slathering themselves in sunscreen to reduce their risk of getting cancer. Despite this, cancer rates are increasing. So it doesn't seem like sunscreen is helping that much at all.

If I'm reading your question correctly, your reasoning depends on certain people being doomed to get cancer no matter what they do. But we can't infer that from the passage -- if sunscreen is effective, then it should help people who are predisposed to cancer to avoid developing the disease.

(E) tells us that these people are using sunscreen. Combined with the info from the passage, we can infer that sunscreen isn't particularly effective. This supports the author's argument, so we can eliminate (E).

I hope that helps!
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Researchers announced recently that over the past 25 years the incidence of skin cancer caused by exposure to harmful rays from the sun has continued to grow in spite of the increasingly widespread use of sunscreens. This shows that using sunscreen is unlikely to reduce a person’s risk of developing such skin cancer.

Which one of the following, if true, most weakens the argument?

(A) Most people who purchase a sunscreen product will not purchase the most expensive brand available.
(B) Skin cancer generally develops among the very old as a result of sunburns experienced when very young.
(C) The development of sunscreens by pharmaceutical companies was based upon research conducted by dermatologists.
(D) People who know that they are especially susceptible to skin cancer are generally disinclined to spend a large amount of time in the sun.
(E) Those who use sunscreens most regularly are people who believe themselves to be most susceptible to skin cancer.

Since the conclusion deals sunscreen's inability to reduce risk of skin cancer, we need a choice that touches upon that aspect keeping in mind that the study was done for past 25 years. B nicely gives us a perspective about what might be a possible reason behind increase of incidences of skin cancer. E slight confuses in that that a belief of people who use sunscreen regularly might weaken but that's not the case here. Those people are extra cautious as E suggests thus it never touches upon sunscreen inability.

Answer B.
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