- A company has three departments: Sales, Support, and Engineering. Every manager works in either Sales or Engineering. No one in Support is a manager. Some people in Sales are not managers. Priya is a manager. Sam works in Support. Which one of the following must be true on the basis of the information above?
Answer: Priya does not work in Support.
The company's departmental structure shows that all managers work in either Sales or Engineering, while no one in Support is a manager. Priya is a manager, so she must work in Sales or Engineering. Since Support contains no managers, Priya cannot work in Support. Sam works in Support, confirming that he is not a manager (consistent with the rule). Choice A is tempting because managers could be in Sales, but they could also be in Engineering - we can't determine which. However, we can definitively exclude Support for Priya based on her manager status. This demonstrates how exclusionary rules about roles and departments can create certain negative inferences even when positive placement remains uncertain.
- Which of the following can be inferred from the information above?
Answer: Exactly 175 runners finished the race.
Twenty registrants did not start (10 percent of 200), leaving 180 starters; with five dropping out, 175 finished. All other options contradict the stated numbers.
- The information above supports which of the following conclusions?
Answer: At least some respondents own both a car and a bicycle.
If 40 percent of bicycle owners do not own a car, then 60 percent do own a car, so some respondents own both. The other options are not supported or contradict the given percentages.
- Which of the following can be inferred from the information above?
Answer: Dana cannot obtain a free repair under the warranty.
Registration after 30 days is impossible and only registered devices are eligible for free repair, so Dana cannot receive a free repair under the warranty. The other choices introduce causes, promises, or impossibilities not established.
- At a small film festival, each screening requires exactly one projectionist. Maya, Theo, and Lin are the only projectionists available. Maya is scheduled for the 1 p.m. screening. Theo is scheduled for the 3 p.m. screening. Lin cannot work any screening that starts before 3 p.m. No projectionist can work two screenings in the same day. The festival has exactly three screenings: 1 p.m., 3 p.m., and 5 p.m. Each screening must be staffed by one of the three projectionists.
Which one of the following can be properly inferred from the statements above?
Answer: Lin is scheduled for the 5 p.m. screening.
As an experienced LSAT tutor, let's break down this inference question by summarizing the key facts: three screenings at 1 p.m., 3 p.m., and 5 p.m. need staffing by Maya, Theo, or Lin, with Maya at 1 p.m., Theo at 3 p.m., Lin unable to work before 3 p.m., and no one handling multiple shifts. In must-be-true questions, we seek conclusions logically guaranteed by the information, without adding assumptions. With Maya and Theo already assigned, the 5 p.m. slot must go to Lin, who is available then, making choice A necessarily true. A tempting wrong answer like choice D might appeal if one overlooks Theo's assignment and thinks Lin could take 3 p.m., but that's not forced since Theo is explicitly at 3 p.m. Remember, correct inferences cannot require assumptions and must follow directly from the given constraints.
- Which of the following is most strongly supported by the statements above?
Answer: Q2 profit dollars were lower than Q1 profit dollars.
With revenue up 10 percent but margin down from 20 percent to 18 percent, profit changed from 0.20R to 0.18(1.10R) = 0.198R, which is lower. The other options introduce claims not entailed by the data or contradict it.
- A school has four clubs: chess, drama, robotics, and debate. Every student who is in robotics is also in debate. No student is in both chess and debate. Some students are in drama and debate. Talia is in robotics. Which one of the following must be true on the basis of the information above?
Answer: Talia is in debate.
The club membership rules create a logical chain: robotics → debate, and chess and debate are mutually exclusive. Talia is in robotics, so by the first rule, she must also be in debate. This is a direct application of conditional logic (if robotics, then debate). We cannot determine from the given information whether Talia is also in drama, since some students are in both drama and debate, but this isn't required. Choice A is tempting because we might wonder about other club possibilities, but the conditional statement 'every student who is in robotics is also in debate' creates a definitive logical requirement. This demonstrates the power of universal conditional statements in logical reasoning - they create non-negotiable logical requirements that lead to certain inferences.
- Which of the following can be inferred from the information above?
Answer: The museum admitted at least 500 visitors in June.
There were 300 paid admissions plus 200 guest-pass admissions, so admissions totaled at least 500. The other statements add unwarranted claims about members, totals above 500, pricing changes, or losses.
- Which of the following is best supported by the information above?
Answer: A 20-year-old student who purchases on Tuesday without a valid student ID will pay full price.
Without a valid student ID and not being 65 or older, the 20-year-old meets no discount requirement and thus pays full price. The other options introduce unsupported assumptions about which discount applies or imply discounts when requirements are unmet.
- All mentors are teachers. Some teachers are coaches. No coaches are mentors. Most supported?
Answer: Some teachers are not mentors.
From 'some teachers are coaches' and 'no coaches are mentors,' those teachers who are coaches cannot be mentors. So some teachers are not mentors. The tempting wrong answer is 'some teachers are mentors' because 'all mentors are teachers' may look reversible, but it does not establish that any teacher is a mentor.
- Which of the following can be inferred from the information above?
Answer: At least 250 vehicles received one or more overnight parking tickets in June.
With 500 tickets and no vehicle receiving more than two, at least 250 vehicles must have been ticketed. The other statements assert exact counts, unrelated booting, or month-wide rules not supported by the facts.
- A museum offers guided tours in three languages: English, French, and Spanish. Each tour is offered in exactly one language. All French tours are on weekends. No Spanish tours are on weekends. Tour T is on a weekend. Tour U is not on a weekend. Tour V is in Spanish. Tour W is in French. The museum offers tours only on weekdays or weekends, and each tour is scheduled for exactly one of those.
Which one of the following can be properly inferred from the statements above?
Answer: Tour T is not in Spanish.
In this inference setup, key facts include French tours → weekends, Spanish → not weekends, T on weekend, U not on weekend, V Spanish, W French, each tour in one language and on weekday or weekend. Must-be-true statements are logically guaranteed without extra assumptions. T on weekend and Spanish → not weekend yield, by contrapositive, weekend → not Spanish, making T not Spanish and choice A necessarily true. A tempting wrong answer like C (T French) might seem plausible since French are on weekends, but T could be English, so it's not forced. Correct inferences cannot require assumptions and must derive directly from conditionals and contrapositives.
- Bell rings only if pump runs, and pump runs only if valve opens. What follows?
Answer: If bell rings, valve opens.
Bell rings only if pump runs means bell rings implies pump runs. Pump runs only if valve opens means pump runs implies valve opens. So if the bell rings, the pump runs, and that means the valve opens. The tempting mistake is reversing the logic to say valve opens implies bell rings, but the arrows only go one way.
- A science fair awards ribbons in three colors: gold, silver, and bronze. No project receives more than one ribbon. Every project that receives gold is judged in the advanced division. Some projects judged in the advanced division receive silver. Project Q was not judged in the advanced division. Which one of the following must be true on the basis of the information above?
Answer: Project Q did not receive gold.
The science fair ribbon system establishes that all gold-ribbon projects are judged in the advanced division, while some advanced division projects receive silver. Project Q was not judged in the advanced division. By contrapositive reasoning, since all gold recipients are in advanced division, any project not in advanced division cannot have received gold. Therefore, Project Q did not receive gold. Choice A is tempting because bronze is a possibility, but we cannot determine the specific ribbon color - only that it wasn't gold. This problem illustrates the power of contrapositive reasoning in eliminating possibilities. When 'all A are B' and something is 'not B,' it cannot be A.
- 60% of City A residents favor the plan. 40% of City B residents favor it. City A has more residents. Most supported?
Answer: A has more supporters than B.
Since City A has more residents and a higher percentage of supporters, the number of supporters in A must be greater than in B. For example, if A has 1,000 residents and B has 900, then A has 600 supporters and B has 360. The tempting wrong answer is that A has fewer opponents than B, but that depends on the exact populations and is not guaranteed.
- A transit card can be used on buses, trains, or ferries. Every ride on a ferry requires a reservation. No bus ride requires a reservation. Some train rides require a reservation and some do not. Ride R required a reservation and was either a bus ride or a train ride. Which one of the following must be true on the basis of the information above?
Answer: Ride R was a train ride.
The transit card rules establish that ferry rides require reservations, bus rides don't require reservations, and train rides are mixed (some require reservations, some don't). Ride R required a reservation and was either a bus or train ride. Since bus rides don't require reservations, and R did require a reservation, R cannot have been a bus ride. Therefore, R must have been a train ride. This is a straightforward application of exclusionary logic - when one option is ruled out by incompatible characteristics, the remaining option must be correct. Choice A is impossible because bus rides don't require reservations. This demonstrates how definitive rules about requirements can eliminate possibilities and force specific conclusions.
- A local ordinance requires that all buildings within the city limits must have smoke detectors installed on every floor. A recent inspection found that 90% of buildings complied with this regulation. Which one of the following must be true on the basis of the information above?
Answer: 10% of buildings within the city limits do not have smoke detectors on every floor.
The stimulus establishes that all buildings within city limits must have smoke detectors on every floor, but only 90% actually comply with this regulation. This directly means that 10% of buildings within the city limits do not have smoke detectors on every floor - they are the non-compliant buildings identified in the inspection. The information is straightforward: if 90% comply, then 10% don't comply. Choice D is tempting because it seems logical that some buildings might have partial compliance, but the stimulus doesn't specify the nature of non-compliance, only that 10% don't meet the full requirement. In inference questions involving percentages and compliance, focus on what the numbers directly tell us rather than speculating about specific types of non-compliance.
- Which of the following can be inferred from the information above?
Answer: Exactly 18 boxes contained apples.
With 30 total boxes and 12 pear boxes, the remaining 18 boxes must have contained apples. B, C, and E make claims about quantities of fruit that are not established by the facts. D contradicts the stated rule that no mixed boxes were offered.
- A training program has three levels: beginner, intermediate, and advanced. Everyone in the advanced level has completed the intermediate level. No one in the beginner level has completed the intermediate level. Some intermediate participants have completed a capstone project. Lee has completed the intermediate level and is enrolled in exactly one level. Which one of the following must be true on the basis of the information above?
Answer: Lee is enrolled in the intermediate level or the advanced level.
The training program's level structure establishes that advanced level participants have completed intermediate, while beginner level participants have not completed intermediate. Lee has completed the intermediate level and is enrolled in exactly one level. Since beginner level participants haven't completed intermediate, and Lee has completed intermediate, Lee cannot be in the beginner level. Since everyone is in exactly one level, Lee must be in either intermediate or advanced level. Choice A is impossible because beginner participants haven't completed intermediate level. The completion of intermediate level eliminates the beginner possibility while allowing for either intermediate or advanced enrollment. This shows how prerequisite completion can eliminate certain level placements while leaving others possible.
- A wildlife survey in a forest recorded sightings of 200 deer, 150 foxes, and 300 rabbits. It was noted that 100 of the deer were seen near water sources. Which one of the following must be true on the basis of the information above?
Answer: At least half of the deer were not seen near water sources.
The stimulus states that 200 deer were recorded, and 100 of them were seen near water sources. This directly means that 100 deer were not seen near water sources (200 - 100 = 100). Since 100 out of 200 represents exactly half, we can conclude that at least half of the deer were not seen near water sources. The information about foxes and rabbits provides context but doesn't affect this mathematical relationship about deer distribution. Choice E is tempting because it's technically true (exactly 100 deer were seen away from water), but choice A captures the proportional relationship more precisely using 'at least half.' In numerical inference questions, calculate the direct mathematical relationships and express them in terms that capture the logical requirement.
