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
Solution
Passage Visualization
| Passage Statement | Visualization and Linkage |
|---|---|
| Most stores in our town with fewer than five employees are owned by women. | Establishes a general pattern for small stores Example: If there are 100 stores with <5 employees, then 60-80 are owned by women Pattern: Small stores ā mostly women-ownedSets expectation for what we should find in any subset of small stores |
| Every antique store in our town has fewer than five employees. | Categorizes all antique stores as “small stores” Example: All 10 antique stores have 1-4 employees each Antique stores = subset of small storesBased on Statement 1, we would expect most antique stores to be women-owned |
| However, none of the antique stores in our town are owned by women. | Reveals a complete contradiction to the expected pattern Example: 0 out of 10 antique stores are women-owned (0%) Expected: 60-80% women-owned | Reality: 0% women-ownedAntique stores are exceptional outliers among small stores |
| Overall Implication | For the general pattern “most small stores are women-owned” to remain true despite antique stores being 0% women-owned, the non-antique small stores must have an even higher concentration of women ownership to compensate for this gap. Example: If 70% of all small stores are women-owned, but antique stores (10 stores) contribute 0%, then the remaining 90 non-antique small stores must be 78% women-owned to maintain the overall majority. |
Valid Inferences
Inference: Most of the stores in Advik’s town that have fewer than five employees and are not antique stores are owned by women.
Supporting Logic: Since most stores with fewer than five employees are owned by women, and every antique store has fewer than five employees but none are owned by women, the non-antique stores with fewer than five employees must have a higher rate of women ownership than the overall average to compensate for the complete absence of women-owned antique stores.
Clarification Note: This inference follows from mathematical necessity – if antique stores contribute 0% to women ownership while being part of a group that is “mostly” women-owned, the remaining stores in that group must exceed 50% women ownership to maintain the majority pattern.
Answer Choices Explained
A. have fewer than five employees are not antique stores
This is CORRECT. Here’s why: We know most stores with fewer than 5 employees are owned by women, but ALL antique stores have fewer than 5 employees and NONE are owned by women. For the ‘most’ pattern to hold true mathematically, the majority of small stores cannot be antique stores (since antique stores contribute 0% to women ownership). If antique stores made up most small stores, then most small stores would not be women-owned, contradicting our first premise.
B. are not owned by women are antique stores
This is INCORRECT. This suggests most stores not owned by women are antique stores. But we don’t have enough information to conclude this. There could be many non-women-owned stores that aren’t antique stores (like larger stores with 5+ employees or other types of small stores).
C. have five or more employees are not owned by women
This is INCORRECT. We have no information about stores with 5 or more employees and their ownership patterns. The argument only discusses stores with fewer than 5 employees.
D. are not antique stores are owned by women
This is INCORRECT. This is too broad. While we can conclude that most small non-antique stores are likely women-owned, we can’t say most of ALL non-antique stores are women-owned (since this would include larger stores about which we know nothing).
E. are owned by women have fewer than five employees
This is INCORRECT. This suggests most women-owned stores are small stores. But the argument tells us about small stores being mostly women-owned, not about women-owned stores being mostly small. We can’t reverse the relationship without additional information.
