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

Question

Advik: Most stores in our town with fewer than five employees are owned by women. Every antique store in our town has fewer than five employees. However, none of the antique stores in our town are owned by women.

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
B. are not owned by women are antique stores
C. have five or more employees are not owned by women
D. are not antique stores are owned by women
E. are owned by women have fewer than five employees

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Official Answer

A

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gmatophobia · Accepted Answer

Advik's statements:

Most stores with fewer than five employees are owned by women. 
 Every antique store in our town has fewer than five employees. 
 None of the antique stores in our town are owned by women.

From these statements, we can infer that most of the stores in Advik's town that have fewer than five employees must not be antique stores.

To understand this better let's take the following example -

Number of stores in Advik's town that have fewer than five employees = 10 
 Number of stores in Advik's town that have fewer than five employees and are owned by women >= 6 
 We know of the 4 remaining stores, some of the stores are antique stores. This is because none of the antique stores in Advik's town are owned by women. 
 Therefore, most of the stores with fewer than five employees are not antique stores. These are the stores that are owned by women.

A. have fewer than five employees are not antique stores

Complete Statement -

Most of the stores in Advik's town that have fewer than five employees are not antique stores.

This could be true based on the second statement. If every antique store has fewer than five employees, then most stores with fewer than five employees are not antique stores. Let's keep this.

B. are now owned by women are antique stores

Complete Statement -

Most of the stores in Advik's town that are now owned by women are antique stores.

This contradicts the information presented in the premise. The premise states that none of the antique stores are owned by women. So, this statement is not necessarily true.

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

Complete Statement -

Most of the stores in Advik's town that have five or more employees are not owned by women.

There is no information presented on the stores that have five or more employees. Hence this statement cannot be concluded.

D. are not antique stores are owned by women

Complete Statement -

Most of the stores in Advik's town that are not antique stores are owned by women.

We cannot conclude this as we are only presented with information on the ownership of stores that have fewer than five employees. However, this statement is regarding " most of the stores in Advik's town ". As we don't have any information on stores that have five or more employees, we cannot conclude this statement.

E. are owned by women have fewer than five employees

Complete Statement -

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

This statement cannot be inferred because we know from the premise that most stores with fewer than five employees are owned by women. Hence, we are presented with information about a subset of stores that are owned by women. As we don't have any information on stores that have five or more employees, we cannot infer this option.

Option A

GmatKnightTutor · Answer

The passage talks about a town in which most of the stores with 1-4 employees are owned by women. That all the antique stories have 1-4 employees but that none of the antique stores are owned by women.

We're asked to look for something that is ALSO true about most stores in this town.

(A) is the answer. If I say you own most of the marbles in the world but that you have no red marbles, that can only be possible if non-red marbles make up a majority of the total. If red marbles made up 90% of all marbles, it would not be possible for you to own the majority of all marbles with the remaining 10%. Similarly, if you say that MOST of the 1-4 employee stores are owned by women... but that a certain type of 1-4 employee store (antique stores) are not owned by women at all, that would mean the OTHER 1-4 employee stores would have to make up the majority of total 1-4 employee stores for the math to work. It would not be possible for women to be most of the owners of 1-4 employee stores otherwise.

Amobnc · Answer

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

MartyMurray · Answer

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

MBAToronto2024 · Answer

KarishmaB  what's wrong with option D?

KarishmaB · Answer

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.

Attachment:

Screenshot 2024-11-18 at 2.49.03 PM.png

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)

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Raman109 · Answer

Advik: Most stores in our town with fewer than five employees are owned by women. Every antique store in our town has fewer than five employees. However, none of the antique stores in our town are owned by women.

Take < 5 employees as group A
>= 5 employees as group B

So in group A, most are owned by women. 
Antique stores are part of group A but are not part of the "most"

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 - True. 
B. are not owned by women are antique stores - We don't know. 
C. have five or more employees are not owned by women - No info on Group B - out of scope.
D. are not antique stores are owned by women - We don't know about group B. 
E. are owned by women have fewer than five employees - It uses all the words but reverses the logic. We know most in group 1 are owned by women. Not that whatever is owned by women have less than 5 employees. What if there are 10 people in group A and 5 million in group B and most of the group B is also owned by women? Wrong.

VasundharaS · Answer

Why not D? This is crazy I don't understand :'(

anjanaroy · Answer

I still think E is the correct option as " This    must be true   . Since most stores with fewer than five employees are owned by women, and    no antique stores    (which are a subset of stores with fewer than five employees) are owned by women, the stores owned by women must be from the    non-antique    subset of stores with fewer than five employees. So,    all stores owned by women must have fewer than five employees   . " Whereas the Option A could be true  but not necessarily. All antique stores have fewer than five employees, but that doesn't mean most stores with fewer than five employees are not antique stores. This is not logically required.

egmat · Answer

This is a classic GMAT Critical Reasoning inference question that tests your ability to identify what must logically follow from a set of premises. Let me break down the logical structure to help you see the solution clearly.

Core Logic Analysis:
Step 1: Map the Given Information

Let's organize what Advik tells us:
Fact 1: Most stores with <5 employees → owned by women
Fact 2: ALL antique stores → have <5 employees
Fact 3: NO antique stores → owned by women

Step 2: Identify the Critical Contradiction

Here's where it gets interesting. Notice that:

Antique stores are a subset of stores with <5 employees (from Fact 2)
But antique stores have 0% women ownership (from Fact 3)
Yet the overall group has "most" (>50%) women ownership (from Fact 1)

Step 3: Apply Mathematical Logic
For the math to work, if antique stores contribute 0% to women ownership, and the overall average must still be >50%, then:

Antique stores must be a minority of all small stores
The non-antique small stores must compensate with higher women ownership

Think of it this way: If you have 100 small stores and 70 are women-owned, but we know ALL antique stores (let's say 20) are NOT women-owned, then those 70 women-owned stores must come from the remaining 80 non-antique stores.

Step 4: Evaluate Answer Choice A

"Most stores that have fewer than five employees are not antique stores"

This must be true! If antique stores were the majority of small stores, and none are women-owned, then most small stores would NOT be women-owned - contradicting Fact 1.
Answer: A

The other choices fail because:

B, D, E: Make claims we can't support with the given information
C: Discusses stores with 5+ employees, which we know nothing about

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Goldenfuture · Answer

I don't understand how D is in-correct. 
See we are already told most stores are owned by women - so they have 50%+ 
Now none of Antique stores are owned by women - so that that as a% 
100-51% = 49% this a sits in this 49% - let this be 0.5%
Now we are simply asked if women own majority of 100-a%
And the answer is a hands down yes = 100-0.5% = 99.5%
50% of this is definitely 49.75%, which is less tham 50%+
Hence women do own majority or most of the non-antique stores of Advik's town - where is this reasoning wrong?
 Bunuel   KarishmaB

Goldenfuture · Answer

Okay I understand now. I am presuming in the venn diagram I made only shops with less than 5 employees and option D does not things so - its larger and all shops are added - less than 5 and more than 5

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

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GMAT Critical Reasoning (CR) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards