Hard LSAT Inference Practice Test Practice Questions

Concept Explanation

An LSAT inference is a statement that must be true based solely on the information provided in the stimulus, without requiring any outside assumptions. Unlike assumptions or strengthen questions, inference questions do not ask you to fix an argument; instead, they require you to find a logical consequence of the given premises. In the context of a Hard LSAT Inference Practice Test, these questions often involve complex conditional logic, formal quantifiers like "most" or "some," and subtle distinctions in language that can lead to common traps. Successful test-takers focus on the "Must Be True" standard, where even the slightest possibility of a statement being false is enough to disqualify an answer choice. To navigate these high-difficulty items, you should look for the overlap between different statements in the stimulus, often referred to as the "bridge" that connects disparate facts into a single, valid conclusion.

Solved Examples

1. Example 1: Conditional Chains
   Stimulus: If a company invests in renewable energy, it will reduce its long-term operational costs. Any company that reduces its long-term operational costs will see an increase in its stock valuation. Some companies that see an increase in stock valuation are also leaders in corporate social responsibility.
   Analysis:
   1. Identify the formal logic: Invest $\rightarrow$ Reduce Costs $\rightarrow$ Increase Valuation.
   2. Combine them: Invest $\rightarrow$ Increase Valuation.
   3. The "some" statement (Valuation $\rightarrow$ CSR) cannot be used to prove that renewable energy investors are CSR leaders, as "some" is not reversible in a way that creates a chain.
   4. Correct Inference: Any company that invests in renewable energy will see an increase in its stock valuation.
2. Example 2: Quantifier Overlap
   Stimulus: Most architects at the firm are proficient in CAD software. More than half of the architects at the firm have over ten years of experience.
   Analysis:
   1. Let the total number of architects be $n$.
   2. CAD group $> 0.5n$. Experience group $> 0.5n$.
   3. Because the sum of these two groups ($> 1.0n$) exceeds the total number of architects, there must be an overlap.
   4. Correct Inference: At least one architect at the firm is both proficient in CAD software and has over ten years of experience.
3. Example 3: The Negative Constraint
   Stimulus: No person who is afraid of heights can be a professional mountain guide. Every professional mountain guide must undergo rigorous safety training. Sarah is afraid of heights.
   Analysis:
   1. Afraid $\rightarrow$ NOT Guide.
   2. Guide $\rightarrow$ Training.
   3. Sarah is Afraid, so Sarah is NOT a Guide.
   4. Note: We cannot conclude Sarah hasn't had training; she just isn't a professional guide.
   5. Correct Inference: Sarah is not a professional mountain guide.

Practice Questions

1. All successful entrepreneurs possess a high degree of resilience. No one who lacks emotional intelligence can effectively lead a large team for more than five years. Some people who possess a high degree of resilience lack emotional intelligence. If the statements above are true, which one of the following must also be true?
   • Some successful entrepreneurs cannot effectively lead a large team for more than five years.
   • Most resilient people are successful entrepreneurs.
   • Emotional intelligence is a prerequisite for becoming a successful entrepreneur.
   • No successful entrepreneur lacks emotional intelligence.
2. During the last decade, every year that saw an increase in the city's property taxes also saw a decrease in the number of new small business licenses issued. In 2018, the number of new small business licenses issued in the city reached an all-time high. Which one of the following can be properly inferred from the statements above?
   • Property taxes in the city decreased in 2018.
   • Property taxes in the city did not increase in 2018.
   • The city council voted against a property tax hike in 2018.
   • Small businesses are more profitable when property taxes are low.
3. To be eligible for the prestigious Grant Fellowship, an applicant must have published at least two papers in peer-reviewed journals. Furthermore, any applicant who has won a national science award is automatically eligible for the fellowship, regardless of their publication record. Dr. Aris has not published any papers in peer-reviewed journals. If the statements above are true, which one of the following must be true?
   • Dr. Aris is not eligible for the Grant Fellowship.
   • If Dr. Aris is eligible for the Grant Fellowship, she must have won a national science award.
   • Winning a national science award is the only way to become eligible without publishing papers.
   • Dr. Aris will likely win a national science award in the future.

4. Recent studies indicate that most professional athletes who follow a plant-based diet report faster recovery times than they did on a meat-based diet. However, any athlete who consumes excessive processed sugars, regardless of their primary diet, will experience increased inflammation. If these statements are true, which one of the following must also be true?
   • Some athletes who follow a plant-based diet experience increased inflammation.
   • A plant-based diet is the most effective way to reduce recovery time.
   • Athletes who do not consume excessive processed sugars will not experience inflammation.
   • If a professional athlete on a plant-based diet experiences increased inflammation, they might be consuming excessive processed sugars.
5. Whenever the temperature drops below freezing, the local pond freezes over. If the pond is frozen over, the neighborhood children go ice skating. Today, the neighborhood children are not ice skating. Which of the following is a valid inference?
   • The temperature is currently above freezing.
   • The temperature did not drop below freezing today.
   • The pond is not frozen over, but it might be cold.
   • It is currently summer.
6. All members of the board of directors are shareholders in the corporation. Some shareholders are also employees of the corporation. No employee of the corporation is allowed to serve on the audit committee. Which of the following must be true?
   • No member of the board of directors serves on the audit committee.
   • Some shareholders are not allowed to serve on the audit committee.
   • All shareholders are members of the board of directors.
   • Employees who are shareholders are on the board of directors.
7. If the bank's interest rates rise, the housing market will slow down. If the housing market slows down, the local construction industry will lose jobs. The local construction industry has not lost any jobs this year. What can be inferred?
   • Interest rates have remained stable.
   • Interest rates have not risen.
   • The housing market has grown significantly.
   • The bank will likely lower interest rates soon.
8. Most birds in the sanctuary are migratory. All migratory birds in the sanctuary fly south for the winter. Some birds in the sanctuary are endangered species. Which of the following must be true?
   • Some endangered species in the sanctuary fly south for the winter.
   • At least some birds in the sanctuary fly south for the winter.
   • Most endangered species in the sanctuary are migratory.
   • All birds that fly south for the winter are migratory.

Answers & Explanations

1. Answer: Some successful entrepreneurs cannot effectively lead a large team for more than five years.
   Explanation: We know all successful entrepreneurs are resilient. We also know some resilient people lack emotional intelligence. Therefore, some successful entrepreneurs might lack emotional intelligence. Since those who lack emotional intelligence cannot lead a team for 5+ years, it follows that some successful entrepreneurs cannot lead for that duration.
2. Answer: Property taxes in the city did not increase in 2018.
   Explanation: The stimulus sets up a conditional: Tax Increase $\rightarrow$ Decrease in Licenses. The contrapositive is: NOT Decrease in Licenses $\rightarrow$ NOT Tax Increase. Since 2018 saw an all-time high in licenses, there was certainly no decrease. Thus, taxes did not increase.
3. Answer: If Dr. Aris is eligible for the Grant Fellowship, she must have won a national science award.
   Explanation: There are two paths to eligibility: (1) 2+ papers or (2) National Award. Dr. Aris failed path 1. Therefore, for her to be eligible, she must have taken path 2.
4. Answer: If a professional athlete on a plant-based diet experiences increased inflammation, they might be consuming excessive processed sugars.
   Explanation: This is a "could be true" style inference embedded in a "must be true" framework. While it doesn't sound as definitive, it correctly identifies that sugar is a sufficient condition for inflammation, which remains a possibility for any athlete.
5. Answer: The temperature did not drop below freezing today.
   Explanation: Using the LSAT Prep methodology of contrapositives: Skating $\rightarrow$ Frozen $\rightarrow$ Below Freezing. The negation (Not Skating) leads back to Not Frozen and then to Not Below Freezing.
6. Answer: Some shareholders are not allowed to serve on the audit committee.
   Explanation: We are told some shareholders are employees. We are also told no employees can serve on the audit committee. Therefore, those specific shareholders who are employees cannot serve.
7. Answer: Interest rates have not risen.
   Explanation: This is a double contrapositive. No Job Loss $\rightarrow$ No Housing Slowdown $\rightarrow$ No Rate Rise.
8. Answer: At least some birds in the sanctuary fly south for the winter.
   Explanation: Since "most" birds are migratory and "all" migratory birds fly south, there is at least one (and likely many) birds flying south.

Frequently Asked Questions

What is the difference between an inference and an assumption?

An inference is a conclusion that follows logically from the premises provided, whereas an assumption is an unstated piece of information required for an argument to function. Inferences are what you can prove, while assumptions are what the author takes for granted.

How do I handle "most" and "some" in LSAT inference questions?

Treat "some" as meaning "at least one" and "most" as meaning "more than half." You can often combine "most" statements if they refer to the same group, but you generally cannot chain "some" statements together to form a valid conclusion.

Can an inference be a restatement of a premise?

Technically, yes, on the LSAT a restatement of a premise counts as something that "must be true." However, high-difficulty questions usually require you to combine at least two premises to find the correct answer.

Why is the contrapositive so important for inference?

The contrapositive is logically equivalent to the original conditional statement and often provides the "hidden" truth that the test-makers use for the correct answer choice. If $A \rightarrow B$, then $\text{not } B \rightarrow \text{not } A$ is always true and frequently tested.

What makes an inference question "hard"?

Hard inference questions often use abstract language, multiple conditional chains, or "soft" quantifiers like "many" or "few" that are designed to trick you into making unwarranted assumptions. They may also use a similar logic structure to other graduate exams but with more rigorous standards for what constitutes a "must be true" answer.