Inference
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LSAT Logical Reasoning › Inference
In a city, 75% of the population uses public transportation, while 40% of those using public transportation report dissatisfaction with the service. Which one of the following must be true on the basis of the information above?
At least 30% of the city's population is dissatisfied with public transportation.
Public transportation is used by more people than those who own cars.
More people are dissatisfied with public transportation than are satisfied.
Some people who use public transportation are satisfied with the service.
The majority of the population is satisfied with public transportation.
Explanation
The stimulus tells us that 75% of the population uses public transportation, and 40% of those users report dissatisfaction. This means 60% of public transportation users are satisfied with the service. Since 75% use public transportation and 60% of those users are satisfied, there definitely exist people who both use public transportation and are satisfied with it. The exact number would be 60% of 75% of the population, which is positive. Choice A is tempting because it calculates 40% of 75% (approximately 30% of total population), but this represents dissatisfied users, not necessarily those who don't use public transport. When dealing with nested percentages, carefully track which group each percentage refers to and what logical relationships must exist.
The information above supports which of the following conclusions?
At least some respondents own both a car and a bicycle.
Fewer than half of respondents own a car.
Most respondents own both a car and a bicycle.
No respondent owns neither a car nor a bicycle.
All bicycle owners also own cars.
Explanation
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.
The information above most strongly supports which of the following?
A factory that files a timely report will not be audited.
A factory that reports an excess will always pay less than a factory that fails to file but is not audited.
A factory that exceeds the legal threshold, fails to file, and is caught by an audit will be fined more than it would have been fined had it filed with the same emissions.
Any factory that fails to file will be fined.
Audits occur only when reports indicate an excess.
Explanation
By rule, an audit-detected excess after failing to file yields a fine twice the reported-violation fine for the same excess. The other choices contradict or go beyond the stated audit and fining procedures.
Which of the following can be inferred from the information above?
Exactly five unregistered runners finished.
Exactly 175 runners finished the race.
More than 25 runners did not start.
Fewer than 170 runners finished the race.
All 200 registrants started the race.
Explanation
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.
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?
Ride R was a bus ride.
No train rides require reservations.
Ride R was a ferry ride.
Ride R was a train ride.
All rides that require reservations are ferry rides.
Explanation
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.
Which of the following can be inferred from the information above?
Non-students must leave the library by 10 p.m.
Study rooms can be reserved only in person at the front desk.
Students may eat in any study room after 10 p.m.
A visitor without a university ID who arrives at 11 p.m. will be denied entry.
The cafe remains open until 10 p.m. during finals week.
Explanation
After 10 p.m., only students with valid IDs are admitted, so a visitor without one arriving at 11 p.m. cannot enter. The other options add assumptions about eating, departures, reservation methods, or cafe hours not supported by the notice.
Which of the following is most strongly supported by the information above?
No Placebo-group participant attended all three visits.
At most 120 Drug-group participants attended any visit.
At least 30 Drug-group participants failed to complete all three visits.
Exactly 30 Drug-group participants missed the first visit.
Fewer than 140 participants attended the second visit.
Explanation
If 140 completed all visits and 20 of those were Placebo, then 120 Drug participants completed all visits. Since 150 participants were assigned to the Drug group, at least 30 Drug participants did not complete. A, B, and E assert specific visit attendance counts not established, and C contradicts the stated number of Placebo completers.
The information above most strongly supports which of the following?
Fewer than half of all employees attended the seminar.
At least one contractor attended the seminar.
Exactly 50 non-manager staff members did not attend the seminar.
More contractors than managers attended the seminar.
All contractors failed to attend the seminar.
Explanation
Staff total 100 (120 minus 20 contractors); with 50 staff attending and all 15 managers attending, exactly 50 non-manager staff did not attend. The other choices speculate about contractor attendance or totals not fixed by the facts.
Which of the following can be properly inferred from the information above?
No applicant with fewer than five publications applied.
The committee extended the deadline in previous years.
Exactly three applicants met both minimums.
At least three applicants met both minimums by the posted deadline.
Interviews began before the application period ended.
Explanation
Because a deadline extension is mandatory if fewer than three meet both minimums and no extension occurred, at least three applicants met both by the deadline. The other options assert exact counts, contradict the timeline, or add unsupported historical claims.
Which of the following is best supported by the information above?
A 20-year-old student who purchases on Tuesday without a valid student ID will pay full price.
A 70-year-old who purchases on Wednesday will pay full price.
Students always receive 10 percent off regardless of the day or ID.
On Tuesdays, any customer who shows any form of identification receives some discount.
A 70-year-old who presents a valid student ID on Tuesday will receive the student discount rather than the senior discount.
Explanation
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.