Deductive reasoning: Practice 3 (Advanced)

Chain project assignments and constrained selections in two original scenarios.

Instructions for this set

Treat all premises as true. Select the one conclusion or arrangement required by the supplied rules; use no outside assumptions.

No calculator is required. List the constraints, apply the extra condition afresh, and test every option. Use a valid example for could and counterexamples for must.

Answer keys and reasoning checked 20 October 2026. These checks do not establish psychometric validity.

Feedback mode has no time limit or negative marking. The optional timed challenge allows 20 minutes and uses the scoring shown on its rules screen. Those settings are not official assessment rules.

Practise with feedback Optional timed challenge

  1. Four analysts A, B, C and D each take exactly one different project: audit, budget, costing and data. A cannot take audit or budget. B takes audit or data. C cannot take costing. D cannot take data.

    1. If B takes data, which project must A take?
    1. Audit
    2. Budget
    3. Costing
    4. Data

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    Answer: C. Costing

    A can take only costing or data. Once B takes data, the one-project-per-analyst rule leaves costing as A’s only option. C and D can then split audit and budget, so the premise is feasible.
  2. 2. If D takes costing, which project must B take?
    1. Budget
    2. Costing
    3. Data
    4. Audit

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    Answer: D. Audit

    With costing taken, A must take data. B can take only audit or data, so B must take audit. C then takes budget. This chain uses the distinct-project requirement at each step.
  3. 3. Which full project assignment is permitted?
    1. A costing; B data; C audit; D budget
    2. A budget; B audit; C data; D costing
    3. A data; B costing; C audit; D budget
    4. A costing; B audit; C budget; D data

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    Answer: A. A costing; B data; C audit; D budget

    The first assignment gives every analyst a different allowed project. The other choices respectively violate A’s budget restriction, B’s audit-or-data restriction and D’s prohibition on data.
  4. 4. If C takes data, which project must D take?
    1. Audit
    2. Budget
    3. Costing
    4. Data

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    Answer: B. Budget

    C using data forces A to costing and B to audit. Budget is then the only unused project for D. All four assignments satisfy the restrictions, so the condition is possible and the answer is necessary.
  5. 5. Which analyst could take the data project?
    1. D only
    2. B only
    3. A, B or C
    4. All four analysts

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    Answer: C. A, B or C

    A can take data with B audit, C budget and D costing. B can take data with A costing, C audit and D budget. C can take data with A costing, B audit and D budget. D is explicitly excluded.

  6. Exactly three of six proposals A, B, C, D, E and F are selected. If A is selected, B is selected. C and D cannot both be selected. Exactly one of E and F is selected. No other constraints apply.

    6. If A is selected, which proposal must also be selected?
    1. C
    2. D
    3. E
    4. B

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    Answer: D. B

    The selection rule directly requires B whenever A is selected. The third proposal can be E or F, so neither E nor F individually is necessary; C and D cannot fit alongside A, B and the required E-or-F place.
  7. 7. If C and E are selected, which proposal must be the third selection?
    1. B
    2. A
    3. D
    4. F

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    Answer: A. B

    D is excluded by C, F is excluded by E, and A would require B as an additional fourth selection. Only B can fill the third place, and B C E satisfies every original rule.
  8. 8. Which complete group of three proposals is permitted?
    1. A C E
    2. B C F
    3. B C D
    4. B E F

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    Answer: B. B C F

    B C F has three proposals, excludes the forbidden C D pair and includes exactly one of E and F. A C E lacks required B; B C D lacks E or F and includes C D; B E F includes both E and F.
  9. 9. If F is not selected and A is selected, which full group must be selected?
    1. A C E
    2. A B F
    3. A B E
    4. B D E

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    Answer: C. A B E

    Exactly one of E and F is required, so excluding F forces E. Selecting A forces B. These three proposals fill all places, giving A B E and leaving no room for any further proposal.
  10. 10. If both C and D are excluded and A is not selected, which pair of groups lists all permitted selections?
    1. B C E or B D F
    2. A B E or A B F
    3. B E F or A E F
    4. No permitted group exists

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    Answer: D. No permitted group exists

    Only B, E and F remain available, but exactly one of E and F may be selected. At most two proposals can therefore be chosen, falling short of the required three. The added conditions are inconsistent.

Review your method

Return to the deductive reasoning lesson and identify the reasoning step behind each mistake before repeating the set.

Choose your practice difficulty

Difficulty labels describe the steps needed in these teaching sets; they are not validated ability bands. Start with foundation practice and move on after you can explain your method.

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