Let me take a shot at this.
Let's understand the argument first.
Background Info: Two genes, BRCA1 and BRCA2, are linked to hereditary breast cancer.
Premise: Genetic testing, which can detect these genes, is increasing in both accuracy and prevalence. The test is also less painful and invasive than a mammogram, which is typically used to detect early signs of breast cancer.
Conclusion/Argument: Therefore, we can expect the percentage of women who undergo mammograms each year to decrease.
We need to find an assumption on which the argument depends. Assumption by itself should hold the conclusion together and negating this assumption should break the argument/conclusion.
(A) Some women who are tested for BRCA1 and BRCA2 will choose not to undergo a mammogram.
That sounds good - if some women who are tested for these genes choose not to undergo a mammogram, the percentage of women who undergo mammograms each year will decrease. Let's also apply the negation technique here.
On negating A, you get:
No women who are tested for BRCA1 and BRCA2 will choose not to undergo a mammogram.
If this were true, then genetic testing wouldn't affect mammogram rates at all. Let's hold onto A.
Let me clarify how negation works.
When negating an answer choice, you want to create the OPPOSITE meaning.
Let's look at choice A again:
Original: "Some women who are tested for BRCA1 and BRCA2 will choose not to undergo a mammogram"
To negate this, we need the opposite of "some women will choose not to undergo" which would be "NO women will choose not to undergo" or more simply "ALL women will undergo"
So the proper negation would be:
"ALL women who are tested for BRCA1 and BRCA2 will still undergo a mammogram"
The negation you suggested: "Some women who are tested for BRCA1 and BRCA2 will choose not to undergo a mammogram" is actually the same as the original statement, not its negation.
(B) The percentage of women undergoing mammograms each year has remained consistent over the last decade.
This is just another background information and doesn't affect the conclusion in any way => eliminate.
(C) Aside from BRCA1 and BRCA2, there are no other genes that are strongly linked to breast cancer.
Irrelevant, eliminate.
(D) Doctors will continue to recommend regular mammograms for all women at risk of breast cancer, regardless of the results of genetic testing.
This assumption goes against the argument/conclusion => eliminate.
(E) A significant percentage of cases of breast cancer are linked to BRCA1 or BRCA2.
This is a valid assumption for any testing that relies on these two genes. Notice that the first line of the passage states that both these genes are linked to hereditary cancer and that genetic testing can detect them, but it doesn't say if a mammogram can detect them or not. So while it's good to have this information to strengthen our conclusion, it's not an assumption needed for the argument or conclusion to hold true. Let's also apply the negation test here:
A
small percentage of breast cancer cases are linked to BRCA1 or BRCA2.
This does weaken the argument or conclusion a bit, but it still doesn't break it. Our argument is that "percentage of women who undergo mammograms each year to decrease". A small percentage of breast cancer cases linked with the two genes could still result in all of those people choosing genetic testing instead of mammograms and overall percentage of people who do mammogram would as a result, decrease. We're interested in decreasing the number of people who undergo mammogram due to genetic testing, by how much doesn't really matter.
Hence, (A) is the correct answer. Please let me know if this isn't clear or you have any follow ups.