Deductive Reasoning Test

Free Deductive Reasoning Test

1. Question 1 of 10

   All members of the choir can read music. James cannot read music. Which conclusion necessarily follows?

   1. James is not a member of the choir.
   2. James is a member of the choir.
   3. Everyone who can read music is a member of the choir.
   4. James does not enjoy music.
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   Answer: A. James is not a member of the choir.

   This is modus tollens: if every choir member can read music, then anyone who cannot read music cannot be in the choir, so James is not a member. Claiming that he is a member flatly contradicts this. Concluding that everyone who can read music is in the choir reverses the premise, an illicit conversion. Concluding that he does not enjoy music imports a fact the premises never mention.

2. Question 2 of 10

   If a parcel is marked “fragile”, it is placed on the top shelf. The parcel labelled 7 is marked “fragile”. Which conclusion necessarily follows?

   1. Every parcel on the top shelf is marked "fragile".
   2. If a parcel is on the top shelf, it is marked "fragile".
   3. Parcel 7 is placed on the top shelf.
   4. Parcel 7 is the only fragile parcel.
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   Answer: C. Parcel 7 is placed on the top shelf.

   This is modus ponens: parcel 7 is fragile, and fragile parcels go on the top shelf, so parcel 7 is placed there. Claiming that every top-shelf parcel is fragile, or that being on the top shelf implies being fragile, both reverse the rule; that is affirming the consequent, since parcels could sit on that shelf for other reasons. Claiming that parcel 7 is the only fragile parcel invents an exclusivity nothing in the premises supports.

3. Question 3 of 10

   All auditors in the firm are qualified accountants. All qualified accountants must complete annual training. Which conclusion necessarily follows?

   1. All qualified accountants are auditors in the firm.
   2. All auditors in the firm must complete annual training.
   3. Anyone who completes annual training is an auditor.
   4. Some qualified accountants are not auditors.
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   Answer: B. All auditors in the firm must complete annual training.

   Chaining the two “all” statements gives the conclusion by transitivity: auditors are accountants, and accountants complete training, so auditors complete training. Claiming that all accountants are auditors reverses the first premise, and claiming that anyone who trains is an auditor reverses the second, both illicit conversions. Claiming that some accountants are not auditors may be true but is not forced, since the premises allow every accountant to be an auditor.

4. Question 4 of 10

   No delivery driver works in the accounts team. Priya works in the accounts team. Which conclusion necessarily follows?

   1. Some delivery drivers work in the accounts team.
   2. Priya manages the delivery drivers.
   3. Everyone in the accounts team was once a delivery driver.
   4. Priya is not a delivery driver.
   Show the answer

   Answer: D. Priya is not a delivery driver.

   Because no delivery driver is in the accounts team, anyone in that team cannot be a delivery driver, so Priya is not one. Claiming that some delivery drivers work in accounts directly contradicts the first premise. Claiming that Priya manages the drivers imports a relationship never stated. Claiming that everyone in accounts was once a driver makes an unsupported historical claim that also cuts against the stated separation of the two roles.

5. Question 5 of 10

   The shipment left either on Monday or on Tuesday, but not both. It did not leave on Monday. Which conclusion necessarily follows?

   1. The shipment left on Tuesday.
   2. The shipment left on both days.
   3. The shipment did not leave that week at all.
   4. The shipment left on Monday.
   Show the answer

   Answer: A. The shipment left on Tuesday.

   This is a disjunctive syllogism: with exactly one of the two days true, ruling out Monday leaves Tuesday. Claiming that it left on both days contradicts the explicit “but not both”. Claiming that it did not leave at all ignores that the premise guarantees the shipment left on one of the two days. Claiming that it left on Monday contradicts the given fact that it did not.

6. Question 6 of 10

   All technicians carry an access card. Some people who carry an access card work night shifts. Which conclusion necessarily follows?

   1. Some technicians work night shifts.
   2. All night-shift workers are technicians.
   3. Some people who work night shifts carry an access card.
   4. No technician works a night shift.
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   Answer: C. Some people who work night shifts carry an access card.

   A “some” statement can be turned around: “some card-carriers work nights” means “some night workers carry a card”. Concluding that some technicians work nights is the undistributed-middle fallacy, because the card-carrying night workers need not be technicians. Concluding that all night workers are technicians over-generalises a “some” into an “all”. Concluding that no technician works nights denies an overlap the premises neither state nor rule out.

7. Question 7 of 10

   If the invoice is approved, the payment is scheduled. If the payment is scheduled, the supplier is notified. The supplier was not notified. Which conclusion necessarily follows?

   1. The payment was scheduled.
   2. The invoice was not approved.
   3. The invoice was approved but the payment was not scheduled.
   4. The supplier was notified after a delay.
   Show the answer

   Answer: B. The invoice was not approved.

   Work backwards by contrapositive: no notification means no scheduled payment, and no scheduled payment means no approval, so the invoice was not approved. Claiming that the payment was scheduled contradicts that backward chain. Claiming that the invoice was approved but not scheduled is impossible, because approval would have forced scheduling. Claiming that the supplier was notified after a delay contradicts the given fact that no notification happened.

8. Question 8 of 10

   If a candidate scores above 80, they progress to interview. Dana did not score above 80. Which conclusion necessarily follows?

   1. Dana does not progress to interview.
   2. Dana progresses to interview.
   3. Everyone who progresses to interview scored above 80.
   4. It cannot be determined whether Dana progresses to interview.
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   Answer: D. It cannot be determined whether Dana progresses to interview.

   Scoring above 80 is stated as sufficient for progressing, not as the only route, so a lower score leaves the outcome open. Concluding that she does not progress is the denying-the-antecedent error: ruling out the sufficient condition does not rule out the result. Concluding that she does progress is the mirror mistake, assuming some alternative route definitely applied when none is stated. Concluding that everyone who progresses scored above 80 reverses the rule into a necessary condition the premise never claims.

9. Question 9 of 10

   All the graduates on the scheme completed an internship. None of those who completed an internship were hired directly from school. Which conclusion necessarily follows?

   1. Everyone hired directly from school completed an internship.
   2. All interns are graduates on the scheme.
   3. None of the graduates on the scheme were hired directly from school.
   4. Some graduates on the scheme were hired directly from school.
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   Answer: C. None of the graduates on the scheme were hired directly from school.

   The graduates are all interns, and no intern was hired from school, so no graduate was hired from school. Claiming that everyone hired from school completed an internship reverses the second premise, an illicit conversion. Claiming that all interns are scheme graduates reverses the first premise the same way. Claiming that some graduates were hired from school directly contradicts the valid conclusion.

10. Question 10 of 10

    A book is restocked only if it has sold out. The atlas has not sold out. Which conclusion necessarily follows?

    1. The atlas is not restocked.
    2. The atlas is restocked.
    3. Every book that has sold out is restocked.
    4. The atlas will sell out shortly.
    Show the answer

    Answer: A. The atlas is not restocked.

    “Restocked only if sold out” means restocking requires a sell-out, so with no sell-out there is no restock; the atlas is not restocked. Claiming that it is restocked contradicts this. Claiming that every sold-out book is restocked misreads “only if” as “if”, treating a necessary condition as a sufficient one. Claiming that the atlas will sell out shortly predicts a future event the premises give no basis for.