How to Use These
Ten worked items across the four families that appear in almost every logical battery. Each carries the full reasoning and, more usefully, the error it was built to catch.
Attempt each before reading on. One standing instruction applies throughout: reason only from the statements given, never from what you know about the world.
Family 1: Syllogisms
Item 1
All auditors are graduates. Some graduates are accountants.
Which follows? (a) Some auditors are accountants (b) Some accountants are graduates (c) All accountants are graduates (d) Some auditors are not accountants
Answer: (b). "Some graduates are accountants" can be turned around: if some graduates are accountants, then some accountants are graduates. Some statements convert safely.
Why (a) fails. The accountants among the graduates and the auditors among the graduates may be entirely separate groups. Nothing in the premises makes them overlap.
Item 2
All senior analysts have completed the certification. Some people who completed the certification work remotely.
Which follows? (a) Some senior analysts work remotely (b) All certified staff are senior analysts (c) Some remote workers are certified (d) No senior analyst works remotely
Answer: (c). Again the conversion of a some statement, and again it is the only safe move available.
Why (b) fails. "All A are B" does not convert. Every senior analyst being certified says nothing about certified people who are not senior analysts.
Item 3: the undistributed middle
All accountants are numerate. Marisol is numerate.
Therefore Marisol is an accountant? No. Numeracy is a property shared by a far larger group than accountants.
The general rule. Sharing a property with a category never places you inside it. This is the categorical form of the conditional error in Item 4.
Family 2: Conditionals
Item 4: affirming the consequent
If a claim exceeds £10,000, it requires director approval. This claim required director approval.
Did it exceed £10,000? Cannot be determined. Other things may also trigger director approval — an unusual counterparty, a flagged account, a policy exception.
The rule stated in one line. A conditional runs one way. Affirming the consequent is invalid; affirming the antecedent is valid.
Item 5: denying the consequent
If the system flags a transaction, it is reviewed manually. This transaction was not reviewed manually.
Was it flagged? No — validly. If flagging guaranteed review, then no review guarantees no flag.
Why this one matters. Denying the consequent is the valid inference that looks most like the invalid one. It is also the form scientific falsification runs on.
Item 6: necessary versus sufficient
Only staff with security clearance may access the archive. Dariusz accessed the archive.
Which follows? (a) Dariusz has clearance (b) Everyone with clearance accesses the archive (c) Dariusz is senior staff (d) Nothing follows
Answer: (a). "Only X may" establishes clearance as necessary for access, so access implies clearance.
Why (b) fails. Necessary is not sufficient. Clearance permits access; it does not compel it, and most people with clearance have never opened the archive.
Family 3: Analytical Puzzles
Item 7
Five reports — Finance, Legal, Operations, Product, Risk — are presented in order, positions 1 to 5.
- Finance is presented immediately before Legal.
- Risk is presented either first or last.
- Operations is presented third.
- Legal is not presented fifth.
What is the full order?
Answer: Finance, Legal, Operations, Product, Risk. Operations takes position 3, so the adjacent Finance–Legal pair must occupy either 1–2 or 4–5. It cannot be 4–5, because that would put Legal fifth. So Finance is 1 and Legal is 2.
Risk must then be first or last, and first is taken — so Risk is 5, leaving Product at 4.
The method. Place the fixed constraint first, then the block constraint, and let the eliminations cascade. Puzzles are almost always solved from the most restrictive clue backwards.
Item 8
Four candidates — Jonas, Petra, Ravi, Sofia — are interviewed Monday to Thursday, one per day.
- Jonas is interviewed before Petra.
- Ravi is interviewed on Wednesday.
- Petra is not interviewed on Thursday.
Who is interviewed on Thursday?
Answer: Sofia. Petra cannot be Thursday, and Wednesday is Ravi's, so Petra is Monday or Tuesday. Jonas must come before her, so Petra is Tuesday and Jonas is Monday — leaving Thursday for Sofia.
Family 4: Argument Analysis
Item 9: identifying the assumption
"Since we introduced the new onboarding flow, weekly active users have risen by a fifth. We should roll it out to every region."
What does the argument assume? (a) That other regions resemble this one (b) That the flow caused the rise (c) That a fifth is a large increase (d) All of these
Answer: (d) — but (b) is the load-bearing one. The argument treats a sequence in time as a causal relationship, and everything else rests on that.
The habit. Whenever a recommendation follows an observed change, ask what else changed in the same period. A seasonal effect, a marketing campaign, or a competitor's outage would produce the identical chart.
Item 10: weakening the argument
"Employees who attended the optional training scored higher on the year-end review. The training improves performance."
Which most weakens it? (a) The training was expensive (b) Attendance was highest among staff already rated strongly (c) Some attendees scored poorly (d) The reviews were conducted by different managers
Answer: (b). Self-selection dissolves the causal claim entirely — the training would look effective even if it did nothing, because the people who opted in were already the higher performers.
Why the others are weaker. Cost is irrelevant to whether it works. Some attendees scoring poorly is consistent with an average effect. Inconsistent reviewers add noise without explaining the direction of the difference.
Which Family Costs the Most Marks?
Conditionals, by a clear margin — and not because they are difficult.
Affirming the consequent produces an answer that feels entirely solid from the inside. There is no moment of uncertainty to alert you, which is exactly why it survives in professional reasoning long after people have learnt its name.
Analytical puzzles cost the most time, which is a different problem with a different fix: they are worth attempting only after the fast items are banked.
Are Real Test Questions Harder?
Not in logical content. Real papers use the same forms, and the valid inference patterns are a short and closed list.
They are harder in three ways: the wording is longer, so the structure has to be extracted from prose before any reasoning starts; the timing is tighter than feels reasonable; and the distractors are built specifically around the near-miss patterns rather than being obviously wrong.
That last property is the argument for generating your own answer before looking at the options. Reading the options first invites the distractor to do your reasoning for you.