LSAT Quiz: Must Be False

What this quiz covers

This quiz focuses on Must Be False, giving you a quick way to practice the rules, question types, and explanations that matter most for LSAT.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. There are more artists than musicians in the town. (correct answer)
2. Exactly 40 residents are artists.
3. No resident is both an artist and a musician.
4. The number of musicians is greater than the number of artists.
5. All artists in the town are not musicians.

Explanation: In must-be-false questions, we need to identify which statement directly contradicts the established facts. The stimulus establishes clear constraints: 100 total residents, with exactly 60 musicians and therefore exactly 40 artists (since everyone is either one or the other, but not both). Choice A claims there are more artists than musicians, which would require more than 60 artists. However, we know definitively that there are only 40 artists and 60 musicians. This directly contradicts the mathematical certainty established by the facts. Choice D might seem tempting because it states the obvious (60 > 40), but the question asks what must be FALSE, not what must be true. The key insight for must-be-false questions is to look for statements that create mathematical impossibilities given the constraints, not merely unlikely scenarios.

Question 2

1. The number of teachers is greater than the number of students. (correct answer)
2. 15 members are teachers.
3. No member is both a student and a teacher.
4. All students are not teachers.
5. There are more students than teachers.

Explanation: With 50 total members and 35 students, exactly 15 must be teachers. Choice A claims teachers outnumber students, requiring more than 35 teachers. Since we know there are exactly 15 teachers, this statement is mathematically impossible (15 cannot be greater than 35). Choice E accurately reflects the established relationship (students > teachers), but this confirms rather than contradicts our facts. The fundamental principle in must-be-false questions is identifying statements that demand impossible numerical relationships. We need answers that require quantities exceeding the established constraints, not those that merely state obvious or redundant information about the given scenario.

Question 3

1. The number of marketing employees is greater than the number of sales employees. (correct answer)
2. 30 employees work in the marketing department.
3. No employee works in both departments.
4. The sales department has more employees than the marketing department.
5. All employees in marketing do not work in sales.

Explanation: This question establishes precise numerical constraints: 75 total employees with 45 in sales, leaving exactly 30 in marketing. Choice A states that marketing has more employees than sales, which would require marketing to have more than 45 employees. Since we know marketing has exactly 30 employees, this statement creates a mathematical impossibility. The established facts make it impossible for 30 to be greater than 45. Choice D might appear redundant since it states what we already know (sales > marketing), but remember that must-be-false questions seek statements that contradict established facts, not those that confirm them. The critical distinction in must-be-false reasoning is identifying statements that violate the numerical certainties rather than those that merely restate given information.

Question 4

1. There are more reptiles than mammals. (correct answer)
2. 120 animals are reptiles.
3. No animal is both a mammal and a reptile.
4. The number of mammals is greater than the number of reptiles.
5. All reptiles are not mammals.

Explanation: The facts establish 300 total animals with 180 mammals, leaving exactly 120 reptiles. Choice A claims there are more reptiles than mammals, requiring more than 180 reptiles. However, we know definitively there are only 120 reptiles compared to 180 mammals. This creates a direct mathematical contradiction (120 cannot exceed 180). Choice D might seem redundant because it states what we can deduce (mammals > reptiles), but it remains consistent with our established facts. Must-be-false questions demand we identify statements that violate numerical certainties, not those that confirm obvious relationships. The answer must create an arithmetically impossible scenario given the constraints, requiring numbers that exceed what the established totals allow.

Question 5

1. There are more juniors than seniors.
2. 60 participants are seniors.
3. No participant is both a junior and a senior.
4. All seniors are not juniors.
5. The number of seniors is greater than the number of juniors. (correct answer)

Explanation: With 150 total participants and 90 juniors, we know there are exactly 60 seniors. Choice E states that seniors outnumber juniors, which would require more than 90 seniors. Since we have established that there are only 60 seniors, this creates a mathematical impossibility (60 cannot be greater than 90). Choice A correctly identifies that juniors outnumber seniors (90 > 60), but this confirms the established relationship rather than contradicting it. The crucial skill in must-be-false questions is distinguishing between statements that violate the numerical constraints versus those that accurately describe the given relationships. We need statements that create impossible mathematical scenarios, not merely obvious or redundant ones.

Question 6

1. The number of non-vegetarian meals is greater than the number of vegetarian meals. (correct answer)
2. 80 meals are non-vegetarian.
3. No meal is both vegetarian and non-vegetarian.
4. The restaurant served more vegetarian meals than non-vegetarian meals.
5. All non-vegetarian meals are not vegetarian.

Explanation: The stimulus establishes 200 total meals with 120 vegetarian, leaving exactly 80 non-vegetarian meals. Choice A states that non-vegetarian meals outnumber vegetarian meals, which would require more than 120 non-vegetarian meals. Since we know there are only 80 non-vegetarian meals compared to 120 vegetarian ones, this creates a mathematical impossibility (80 cannot exceed 120). Choice D correctly identifies that vegetarian meals outnumber non-vegetarian meals, but this confirms the established relationship. Must-be-false questions require identifying statements that create numerical contradictions with the given facts. The answer must demand quantities that violate the established constraints, making the statement arithmetically impossible rather than merely incorrect or redundant.

Question 7

1. The number of checkers players is greater than the number of chess players. (correct answer)
2. 100 participants play checkers.
3. No participant plays both chess and checkers.
4. All chess players do not play checkers.
5. There are more chess players than checkers players.

Explanation: The established facts show 250 total participants with 150 chess players, leaving exactly 100 checkers players. Choice A claims checkers players outnumber chess players, requiring more than 150 checkers players. Since we know there are only 100 checkers players compared to 150 chess players, this statement is mathematically impossible (100 cannot exceed 150). Choice E correctly states that chess players outnumber checkers players (150 > 100), confirming rather than contradicting our established facts. Must-be-false questions require us to identify statements that create numerical impossibilities with the given constraints. The correct answer must demand quantities that exceed what the established totals permit, making the statement arithmetically contradictory rather than merely obvious.

Question 8

1. The basketball team has more players than the soccer team. (correct answer)
2. 50 students play on the basketball team.
3. No student plays on both teams.
4. The soccer team has more players than the basketball team.
5. All basketball players are not on the soccer team.

Explanation: The stimulus creates definitive constraints: 120 students total, 70 on soccer, therefore exactly 50 on basketball. Choice A claims basketball has more players than soccer, requiring basketball to have more than 70 players. However, we know with mathematical certainty that basketball has exactly 50 players while soccer has 70. This creates a direct contradiction with the established facts (50 cannot be greater than 70). Choice D states the obvious relationship (70 > 50), but this confirms rather than contradicts our facts. In must-be-false questions, we must distinguish between statements that violate mathematical certainties versus those that seem redundant but remain consistent with the given information. The answer must create an impossible scenario, not merely an obvious one.

Question 9

1. Exactly 25 members attended only workshop A.
2. Exactly 22 members attended only workshop B.
3. Exactly 30 members attended only workshop A. (correct answer)
4. Fewer than half the members attended both workshops.
5. More members attended at least one workshop than did not attend any workshop.

Explanation: By inclusion–exclusion, 25 attended only A (38−13) and 22 attended only B (35−13), so exactly 30 attending only A is impossible. The other statements are either true on these numbers or consistent with them.

Question 10

1. Exactly one student failed history.
2. B was one of the two students who passed both tests. (correct answer)
3. A and C both passed both tests.
4. D failed history.
5. B passed history.

Explanation: B failed math, so B cannot be among those who passed both tests. The other statements are consistent with exactly two students passing both and everyone passing at least one test.

Question 11

1. L presents on Monday. (correct answer)
2. N presents on Friday.
3. M presents on Tuesday.
4. K presents on Thursday.
5. J presents on Monday.

Explanation: Enumerating valid schedules shows L must be on Wednesday, Thursday, or Friday, never Monday. The other placements each occur in at least one valid arrangement.

Question 12

1. The budget did not pass.
2. The bylaws were not changed.
3. Some recommendations were adopted.
4. The chair supported adoption of the recommendations. (correct answer)
5. No recommendations were adopted.

Explanation: With at least one no vote, neither the budget passes nor the bylaws change, so not all recommendations can be adopted; thus the chair cannot support adoption (which requires all to be adopted). The other options are possible or entailed by the premises.

Question 13

1. Fewer tickets were sold this year than last. (correct answer)
2. More tickets were sold this year than last.
3. VIP tickets constituted a larger share of tickets this year than last.
4. The average ticket price fell even if the number of VIP tickets increased.
5. The VIP surcharge amount was unchanged from last year.

Explanation: If average price fell while total ticket revenue rose, the number of tickets sold must have increased, so selling fewer tickets is impossible. The other statements could be true or are explicitly allowed by the premises.

Question 14

1. A children's event was held on Tuesday evening.
2. A children's event was held on Thursday evening.
3. A children's event was held on Friday evening.
4. A children's event was held on Monday afternoon. (correct answer)
5. No children's events were held this week.

Explanation: Children's events occur only on days open after 5 p.m. and are always in the evening, so an event on Monday afternoon is impossible. The other options could occur given the hours and the fact that no event is required.

Question 15

1. The number of non-fiction books is greater than the number of fiction books.
2. There are 120 non-fiction books.
3. No book is both fiction and non-fiction.
4. All fiction books are not non-fiction.
5. The library has more fiction books than non-fiction books. (correct answer)

Explanation: The stimulus establishes that there are 200 total books with 80 fiction books, meaning exactly 120 are non-fiction. Choice E claims the library has more fiction than non-fiction books, which would require more than 120 fiction books. Since we know there are exactly 80 fiction books and 120 non-fiction books, this statement is mathematically impossible. Choice A might seem tempting because it correctly states that non-fiction (120) exceeds fiction (80), but this confirms rather than contradicts the established facts. Must-be-false questions require us to identify statements that create numerical impossibilities, not those that accurately reflect the given relationships. The key is recognizing when a statement demands numbers that exceed the established totals.

Question 16

1. X is on Truck 1.
2. Y is on Truck 1.
3. Z is on Truck 2.
4. Y is on Truck 2. (correct answer)
5. Truck 2 carries exactly one crate.

Explanation: The logical constraints make 'Y is on Truck 2' impossible through a chain of necessary implications. We know X cannot be on Truck 2, so X must be on Truck 1. If Y is on Truck 2, then by contrapositive of 'if Y is on Truck 1, then Z is on Truck 2,' we cannot definitively place Z yet. However, 'if Z is on Truck 2, then Y is not on Truck 2' directly contradicts our assumption that Y is on Truck 2. Additionally, 'if Y is not on Truck 2, then Y is on Truck 1' means Y must be somewhere, and the contrapositive tells us if Y is on Truck 2, then Y is not on Truck 1. But we also need each truck to carry at least one crate. With X on Truck 1 and Y on Truck 2, Z could go on either truck. However, the rule 'if Z is on Truck 2, then Y is not on Truck 2' directly prohibits Y and Z from both being on Truck 2, making the scenario impossible. Choice C ('Z is on Truck 2') could work if Y is on Truck 1. Direct contradictory conditionals often create these definitive impossibilities.

Question 17

1. First Aid (A) is chosen.
2. Vegetables (V) is chosen.
3. Native Plants (N) is chosen.
4. Fire (F) is chosen. (correct answer)
5. Exactly two workshops are scheduled.

Explanation: The constraints make 'Fire (F) is chosen' impossible due to incompatible requirements. If Fire is chosen as the safety workshop, then Native Plants is not chosen as the gardening workshop (given rule). Since exactly one gardening workshop must be chosen and Native Plants is not chosen, Vegetables must be chosen. However, 'Vegetables cannot be chosen on the same day as Fire.' This creates a direct contradiction: choosing Fire requires choosing Vegetables (as the only remaining gardening option), but Vegetables cannot be chosen with Fire. Additionally, we have 'Native Plants is chosen if and only if Fire is not chosen,' which means Fire not being chosen is equivalent to Native Plants being chosen. Choice E ('First Aid is chosen') would work: if First Aid is the safety choice, then Vegetables must be chosen as the gardening workshop (given rule), and this combination has no prohibitions. The biconditional relationship between Fire and Native Plants, combined with the exclusion of Vegetables with Fire, creates this impossibility.

Question 18

1. Gita receives arts.
2. Hugo receives science.
3. Faye receives science. (correct answer)
4. Faye receives arts.
5. Hugo does not receive arts.

Explanation: The constraints make 'Faye receives science' impossible due to cascading logical requirements. If Faye receives science, then Gita receives arts (given rule). If Gita receives arts, then Hugo receives science (given rule). But we also have 'if Hugo receives science, then Faye does not receive science.' This creates a direct contradiction: Faye receiving science ultimately requires that Faye not receive science. Additionally, Hugo cannot receive arts, so Hugo must receive science or nothing. Since exactly two scholarships are awarded (one science, one arts) and no student can receive both, we need exactly two different students to receive the scholarships. The logical chain shows that if Faye gets science, then ultimately both Gita gets arts and Hugo gets science, but Hugo getting science prohibits Faye from getting science. Choice A ('Gita receives arts') could work if Hugo gets science and Faye gets nothing. Logical chains that circle back to contradict their starting assumption often indicate must-be-false scenarios.

Question 19

1. Hale attends.
2. Inez attends.
3. Kwan attends.
4. Jori attends.
5. Hale is captain. (correct answer)

Explanation: The logical constraints make 'Hale is captain' impossible through a contradiction chain. If Hale is captain, then Kwan attends (given rule). If Kwan attends, then Hale is not captain (given rule). This creates a direct logical contradiction—Hale being captain both requires and prohibits Kwan's attendance simultaneously. Additionally, we know Jori attends if and only if Kwan does not attend, so if Kwan attends, Jori doesn't. We also have 'if Hale attends, then Inez attends.' So if Hale is captain (and thus attends), Inez must attend. This would give us Hale (captain), Inez, and Kwan attending, with Jori not attending. But the captain cannot be Inez, which this scenario respects. However, the fundamental contradiction between Hale being captain requiring Kwan's attendance while Kwan's attendance prohibits Hale being captain makes choice E definitively false. Circular logical dependencies often signal must-be-false answers in conditional reasoning.

Question 20

1. Science is featured.
2. Mystery is featured.
3. History is featured.
4. Poetry is on the top shelf. (correct answer)
5. Exactly one featured genre is on the top shelf.

Explanation: The constraint 'Poetry cannot be on the top shelf' directly makes 'Poetry is on the top shelf' impossible. This is a straightforward prohibition that definitively eliminates choice D. Additionally, examining the logical structure: exactly three genres are featured from four, and exactly one featured genre goes on the top shelf. The other constraints create dependencies between which genres are featured and which one goes on top, but none override the fundamental restriction on Poetry's shelf placement. For instance, 'if Science is featured, then the top-shelf genre is Science' means Science would claim the top shelf if featured, but this doesn't make Poetry being on top shelf any more possible. Choice A ('Science is featured') could work if the chain of implications is satisfied. The direct prohibitive constraint on Poetry's placement creates an unambiguous must-be-false scenario, unlike more complex logical chains that might have workarounds.