Advik: Most stores in our town with fewer than five employees are owne

Can I get a clearer explanation of why E) is incorrect please?
Thanks!

 
­The statement completed with (E) is:

Most of the stores in Advik's town that are owned by women have fewer than five employees.

That statement is not supported by the passage because the passage provides no information indicating the proportion of stores owned by women that have fewer than five employees.

In other words the passage does not indicate the value of the following:

          \(\frac{\text{women owned stores with fewer than five employees}}{\text{total women owned stores}}\)

In other words, we don't have any information on the characteristics of "most of the stores in Advik's town that are owned by women," such as what this choice says.­

The passage tells us about only the proportion of stores with fewer than five employees owned by women, which is "most stores with fewer than five employees," or more than half. In other words, it tells us the following:

          \(\frac{\text{women owned stores with fewer than five employees}}{\text{total stores with fewer than five employees}} > \frac{1}{2}\) 

KarishmaB what's wrong with option D?

Given:
Most stores in our town with fewer than five employees are owned by women.
Say there are 20 stores with fewer than 5 employees. At least 11 of these are owned by women. Note here that we have no idea about how many stores there are that have more than 5 employees.


Every antique store in our town has fewer than five employees.
So all antique stores are a part of those 20.

However, none of the antique stores in our town are owned by women.
But none of the antique stores are a part of that 'at least 11'.

It works, right? It is possible that exactly 11 of those 20 stores are owned by women and all antique stores are a part of the leftover 9. Or say 12 of those 20 stores are owned by women and all antique stores are a part of the leftover 8 etc.




If Advik's statements are true, then it must also be true that most of the stores in Advik's town that

A. have fewer than five employees are not antique stores

Most of the stores that have fewer than five employees are not antique stores.

This is correct.

"stores that have fewer than five employees" - 20 stores assumed above

So this statement says that "Most of the 20 stores are not antique stores."
This is correct. We saw above that antique stores can be at most 9 of the 20 stores.

B. are not owned by women are antique stores

Most of the stores that are not owned by women are antique stores.

We don't know how many overall stores are not owned by women i.e. are owned by men.
As we see in the Venn diagram above, number of stores owned by men is unknown.


C. have five or more employees are not owned by women

Most of the stores that have five or more employees are not owned by women

We don't know how many stores have 5 or more employees.


D. are not antique stores are owned by women

Most of the stores that are not antique stores are owned by women

We don't know how many stores are outside the green antique stores circle. We don't know how many stores have 5 or more employees and who owns them. Are most of them owned by women or men, we cannot say. Either is possible.


E. are owned by women have fewer than five employees­

Most of the stores that are owned by women have fewer than five employees­.

Again, we don't know how many stores have 5 or more employees and who owns them. As per our example, women own 11 stores with less than 5 employees. Women could own no store with 5 or more employees or they could own 100 stores with 5 or more employees.

Answer (A)

I have discussed how using SETS can help in solving CR questions in the following videos:

https://youtu.be/0uqq17WCJiE
https://youtu.be/XCBp62o70Eg
https://youtu.be/XCBp62o70Eg