Deductive reasoning examples

Deductive vs inductive reasoning

Deductive reasoning starts with rules and works down to a certain conclusion. "All invoices over $1,000 need two signatures. This invoice is $1,400. So it needs two signatures." If the rules are true, the conclusion cannot be false.

Inductive reasoning starts with examples and works up to a likely rule. "The last six invoices over $1,000 had two signatures, so the rule is probably two signatures." The conclusion could still be wrong.

In job tests, inductive questions usually look like shape sequences or number patterns (see our abstract reasoning test and number series guide). Deductive questions are written puzzles with rules. This guide covers the deductive kind. Two habits matter in every example below:

• Treat the rules as true, even if they seem odd in real life.
• Use only the rules. Outside knowledge is the most common reason for a wrong answer.

Ordering and ranking examples

Example 1. Five colleagues compare their sales for the month.

• Priya sold more than Marcus.
• Elena sold less than Tom but more than Priya.
• Zoe sold the least.

Who sold the most, and who came second?

Method: build one line from the highest to the lowest, adding one clue at a time. Clue 2 gives Tom, then Elena, then Priya. Clue 1 puts Marcus below Priya. Clue 3 puts Zoe at the bottom. The full order is Tom, Elena, Priya, Marcus, Zoe. Tom sold the most and Elena came second.

Example 2: the "cannot tell" trap. Box A is heavier than box B. Box C is lighter than box B. Box D is heavier than box C.

• Which box is lightest? C is lighter than B, B is lighter than A, and C is lighter than D. C is the lightest.
• Is D heavier than B? D is only compared with C. It could sit above B or below it. Cannot tell.

Method: draw the items on a vertical line. When a clue links an item to only one other item, mark it with an arrow rather than a fixed spot, so you do not fix a position the rules never gave.

If-then rule examples

Example 3. Two rules from a company policy:

• Every expense over $500 is sent to a manager.
• Every expense sent to a manager is logged in the audit file.

What can you conclude in each case?

• An expense of $650. It is over $500, so it is sent to a manager, so it is logged. It is in the audit file.
• An expense that is not in the audit file. If it had been sent to a manager it would be logged, so it was not sent. If it were over $500 it would have been sent, so it is $500 or less. This backwards step (the contrapositive) is valid.
• An expense that is in the audit file. The rules say what gets logged, not that only manager expenses are logged. Cannot tell whether it is over $500.
• An expense of $300. The rules say nothing about expenses of $500 or less. Cannot tell whether it is logged.

Method: write "over $500 → manager → audit file" as a chain. You may move forward along the arrows, and you may move backwards only with "not" on both ends. Moving backwards without "not", or forwards from a "not", are the two classic traps.

Watch the wording. "Only if" reverses the direction: "a candidate is shortlisted only if they pass the test" means shortlisted → passed, not passed → shortlisted. "Unless" means "if not": "the report goes out on Friday unless the data is late" means if the data is not late, the report goes out on Friday. For all-and-some statements, see our syllogisms guide.

Seating plan examples

Example 4. Farah, Gus, Hana, Ivan and Jo sit in a row of five seats, numbered 1 to 5 from left to right.

• Hana is in seat 3.
• Gus sits immediately to the right of Farah.
• Jo is not in an end seat.
• Ivan sits somewhere to the left of Hana.

Who is in seat 5?

Method: draw five boxes. Place the fixed clue first, then use the narrowest clue to split the problem into cases.

• Hana goes in seat 3.
• Jo is not at an end, so Jo is in seat 2 or seat 4. That gives two cases.
• Case A: Jo in seat 2. Ivan must be left of Hana, and only seat 1 is free there, so Ivan is in seat 1. Seats 4 and 5 are left, side by side, so Farah is in 4 and Gus in 5. Every clue is met.
• Case B: Jo in seat 4. Ivan takes seat 1 or 2, leaving seats 5 and either 2 or 1. Those are never side by side, so Farah and Gus cannot sit together. Case B fails.

The only arrangement is Ivan, Jo, Hana, Farah, Gus. Gus is in seat 5.

The habit that saves time: when a clue allows only two or three positions, try each one. A failed case is not wasted work; it is how you prove the answer.

Scheduling examples

Example 5. Four training sessions (Excel, Safety, Payroll and Ethics) run once each, one a day, Monday to Thursday.

• Safety is on Monday or Thursday.
• Ethics is the day immediately after Excel.
• Payroll is not on Monday or Wednesday.

Method: start with the most restricted item. Payroll can only be on Tuesday or Thursday, so try both.

• Payroll on Tuesday. Monday, Wednesday and Thursday are left. Excel and Ethics need two days in a row, so they take Wednesday and Thursday. Safety is on Monday, which is allowed. Schedule 1: Safety, Payroll, Excel, Ethics.
• Payroll on Thursday. Monday, Tuesday and Wednesday are left. If Excel and Ethics take Monday and Tuesday, Safety lands on Wednesday, which breaks the first rule. So they take Tuesday and Wednesday, and Safety is on Monday. Schedule 2: Safety, Excel, Ethics, Payroll.

Two schedules fit, which is exactly what tests use to ask the next kind of question.

Must be true, could be true or cannot tell

Using the two schedules from Example 5:

• "Safety is on Monday." True in both schedules. Must be true.
• "Excel is on Tuesday." True in Schedule 2 only. Could be true, but not must.
• "Ethics is on Monday." False in both. Cannot be true.
• "On which day is Payroll?" Tuesday or Thursday. Cannot tell.

Method: list every arrangement that fits, then test each option against all of them. "Must" means every arrangement; "could" means at least one.

Example 6: statements instead of a grid. Read the rules, then judge each statement.

• All staff in the Denver office use the new booking system.
• Some staff who use the new booking system work part time.
• No part-time staff attend the Monday planning meeting.

1. "Some Denver staff work part time." The part-time users might all work elsewhere. Cannot tell.
2. "Some booking-system users do not attend the Monday meeting." Some users are part time, and no part-time staff attend. True.
3. "No Denver staff attend the Monday meeting." Nothing links Denver staff to the meeting. Cannot tell.
4. "Every Denver employee uses the new booking system." This restates the first rule. True.

Statement 1 is the classic trap: it sounds likely, but "some users" does not tell you which users.

Common mistakes

• Bringing in real-world knowledge. If the rules say every manager drives a company car, accept it. The question is what follows, not what is realistic.
• Reading "some" as "some but not all". In logic tests, "some" means at least one, and it can include all.
• Running an if-then rule backwards. "If it is over $500, it is logged" does not mean "if it is logged, it is over $500".
• Stopping at the first arrangement that works. A seating or scheduling puzzle may have two solutions. Before you answer a "must be true" question, check whether another arrangement also fits.
• Choosing "false" when the answer is "cannot tell". False means the rules contradict the statement. Cannot tell means the rules are silent.

A speed method for timed tests

Deductive puzzles reward a fixed routine more than raw cleverness:

1. Read the question first, so you know whether you need one position, a full order or a must-be-true check.
2. Turn each rule into shorthand as you read: "F G" for "Gus immediately right of Farah", "P not Mon/Wed", "E = X + 1".
3. Place fixed facts, then the most restricted item. That is usually the fastest route to one or two cases.
4. Test answer options against your sketch, rather than solving everything. Often one clue rules out three options at once.
5. Leave long grids for later. If a puzzle has six or more people and no fixed clue, mark it, move on and come back if there is time.

Some publishers offer deductive reasoning practice of their own: SHL lists a deductive reasoning test among its free candidate practice tests. Our logical reasoning test and critical thinking test let you practice these puzzle types under a timer.