Logical Reasoning Course: Lessons 2026

Lesson 1: How logical reasoning tests work

Some employers ask job applicants to take a logical reasoning test. It checks how well you think: can you spot a pattern, follow a rule, or see what must follow from a set of facts? You need no special knowledge, just a careful method.

The Government of Canada's Skills for Success model describes problem solving as your ability to identify and analyse problems, propose solutions and make decisions. It lists things like seeking patterns, making connections across information, spotting cause and effect, and logical, "if-then" thinking. Logical reasoning tests check these same skills.

This course covers five common question types: number and letter series, deductive questions (syllogisms), ordering and seating puzzles, codes and rules, and patterns in tables or examples. Each of the next lessons covers one type.

Deductive and inductive reasoning

In deductive reasoning, a correct conclusion must be true if the statements are true. Philosophers call such an argument valid. In inductive reasoning, you look at examples, find a rule that is likely, and use it. Because an inductive rule is only likely, check that it fits every example given, not just the first two.

Always treat the statements as true and use only the information given. If a question says "All managers drive red cars", accept it, even if real life is different. Do not add outside knowledge.

A five-step method

1. Read the question. Does it ask what must be true, what could be true, or what comes next?
2. Sketch it. Draw a line of slots, a circle, a table or a Venn diagram on rough paper.
3. Place the fixed facts first, then add the clues that link things together.
4. Test the options. Rule out the ones that break a clue.
5. Check the answer you chose against every statement.

"Must", "could" and "cannot be determined"

• Must be true: true in every arrangement that fits the clues. An option that is only possible is wrong.
• Could be true: true in at least one arrangement that fits the clues.
• Cannot be determined: the clues allow more than one answer. Choose it only after you have found two answers that both fit.

To show that a conclusion does not follow, find a counterexample: one possible case where all the statements are true but the conclusion is false. The conclusion is the claim the other statements support. Words like "so" and "therefore" often come just before it.

Time and test conditions

Work out your average time per question at the start. With 24 questions in 18 minutes you have 1,080 seconds, so 1,080 ÷ 24 = 45 seconds per question. Be careful: 18 ÷ 24 = 0.75 minutes, which is 45 seconds, not 75 seconds.

• The Public Service Commission of Canada advises test takers to read questions carefully, manage their time, and leave time to review their answers.
• In its online tests, a timer shows how much time is left, and the test closes when the time is up.
• You can tick Mark for Review to come back to a question. Marking a question does not affect your score.
• In its supervised online tests, rough paper and pencils are provided. Use them to sketch.
• Accommodation measures are tailored to your situation. Tell the person who invited you to the test as soon as possible.

If you are stuck well past your average time, choose your best answer, mark the question if you can, and move on. After you rule out some options, test each remaining option against every statement before you choose.

Quiz thématique 1 : How logical reasoning tests work

Lesson 2: Number and letter series

A series is a list that follows a rule. Most rules are built from a few simple ideas, so check them in this order.

Step 1: Look at the differences

Subtract each number from the next. In 4, 9, 14, 19 the difference is always +5, so the next number is 24. Differences can also be negative: 81, 72, 63, 54 goes down by 9 each time.

If the differences are not all the same, look at the differences themselves. In 5, 7, 11, 17, 25 the differences are 2, 4, 6, 8. They grow by 2, so the next difference is 10 and the next number is 35. When the differences are 1, 4, 9, 16, they are square numbers (1×1, 2×2, 3×3, 4×4), so the next one is 5 × 5 = 25.

Step 2: Look at multiplying and dividing

If the numbers grow fast, try dividing each number by the one before. 3, 6, 12, 24 doubles each time. In 1, 2, 6, 24, 120 the multiplier grows: × 2, × 3, × 4, × 5, so next is × 6. Some rules use two steps: in 2, 5, 11, 23, each number is doubled and then 1 is added.

Step 3: Look for other common rules

• Square numbers: 1, 4, 9, 16, 25, 36.
• Add the two before: 2, 3, 5, 8, 13, 21 (each number is the sum of the previous two).
• Alternating series: two series take turns. In 10, 3, 12, 6, 14, 9 one series is 10, 12, 14 (+2) and the other is 3, 6, 9 (+3).
• Alternating steps: one series that switches between two steps, such as ÷ 2, then + 2: 100, 50, 52, 26, 28, 14.

Finding the wrong number

Some questions say one number is wrong. Find the rule that fits most of the series, then rebuild it. In 2, 6, 18, 52, 162 the rule × 3 gives 2, 6, 18, 54, 162, so 52 is the wrong number.

Letter series

Turn letters into their positions in the alphabet and solve the number series. After working it out, turn the number back into a letter.

• A, C, E, G = 1, 3, 5, 7. Add 2: next is 9 = I.
• Z, W, T, Q = 26, 23, 20, 17. Subtract 3: next is 14 = N.
• B, D, G, K = 2, 4, 7, 11. The steps grow (+2, +3, +4), so add 5: 16 = P.
• In pairs like AZ, BY, CX, DW, the first letter moves forward and the second moves back: next is EV.
• In letter-number pairs like A1, C3, E5, the number is often the letter's position.

Quiz thématique 2 : Number and letter series

Lesson 3: Deductive reasoning and syllogisms

A syllogism is a short argument: two or more statements (premises) and a conclusion. In a test, you choose the conclusion that must be true if the statements are true. Logic books have long sorted these statements into four kinds.

Draw circles

Draw one circle per group. "All A are B" puts circle A inside circle B. "No A are B" draws them apart. "Some A are B" makes them overlap. Then ask: is there any way to draw the circles so that every statement is true but the conclusion is false? If yes, the conclusion does not have to be true.

Patterns that work

• Chain: All trainees attend the briefing. Everyone at the briefing signs the sheet. So all trainees sign the sheet.
• Member of a group: All guards have first aid. Priya is a guard. So Priya has first aid.
• No + all: No contractor has a staff badge. Everyone in Room 4 is a contractor. So no one in Room 4 has a staff badge.
• Some + all: Some cashiers are students. All students get a discount. So some cashiers get a discount.
• All + some not: All night-shift staff have a pass. Some cleaners have no pass. So some cleaners are not night-shift staff.

Traps to avoid

• Reversing "all": All forklift operators wear boots. Sam wears boots. This does not tell you whether Sam is an operator.
• Two "some" statements: Some drivers are mechanics, and some mechanics are supervisors. Nothing follows about drivers and supervisors.
• Reading "some" as "not all": "Some new hires speak French" does not mean some do not.

If-then statements

Take the rule "If it snows, the crew salts the lot."

Rules can be chained. If high-priority tickets go to Level 2, and Level 2 tickets are reported to a manager, then a ticket not reported to a manager did not go to Level 2, so it was not high priority.

Other key words

• "A only if B" means "if A, then B". "You may enter only if you wear glasses" means anyone who enters wears glasses. Wearing glasses does not guarantee entry.
• "A unless B" means "if not B, then A". "The store opens at 9 unless it is a holiday": if it did not open at 9, it is a holiday.
• "Either A or B, but not both": if one is false, the other is true.

Quiz thématique 3 : Deductive reasoning and syllogisms

Lesson 4: Ordering and seating puzzles

Ordering puzzles give you people or things and a set of clues. You place each one in a position: a place in a line, a floor, a day, a time or a seat.

Build the diagram

1. Draw the slots: 1 to 5 for a line, a circle of seats for a table, or a grid for two features (such as time and room).
2. Write in fixed clues first: "Gus arrived first", "First aid is on Wednesday".
3. Add linked clues: "directly after", "next to", "opposite".
4. Use loose clues last: "earlier than", "not on Monday".
5. If a clue allows two places, try each case and see which one breaks a clue.

Read the words exactly

• Directly / immediately after: the very next place. After / later than: any place further on.
• Next to: on either side, unless the clue gives a side.
• Between: count only the people in the middle, not the two ends.
• Higher number / higher floor: check which end is 1.

Example: Five stops start at the depot. The clinic comes immediately after the bakery, the garage comes before the florist, and the florist is not last. Try the bakery-clinic pair in each spot. Only depot, garage, florist, bakery, clinic works.

Round tables

Seat one person anywhere; this fixes the circle. When people face the centre, the seat to a person's left is the next seat going clockwise (looking down from above), and the seat to their right is the next one counter-clockwise. "Opposite" at a table of six is three seats away.

Must, could and cannot be determined

Some puzzles have more than one arrangement that fits. List them all. A statement must be true if it is true in every arrangement. It could be true if it is true in at least one. If the question asks for one item and the arrangements disagree, the answer cannot be determined. For example, if Pat and Rae are both older than Quinn, but nothing compares Pat and Rae, you cannot tell who is oldest.

Quiz thématique 4 : Ordering and seating puzzles

Lesson 5: Codes, rules and exceptions

Letter codes

Compare the plain word and its code one letter at a time, using alphabet positions from Lesson 2.

• Shift: each letter moves the same number of places. CAT → DBU is +1. MAP → KYN is −2. Shifts wrap around: one place back from A is Z, two places back is Y.
• Reverse: the word is written backwards. LAMP → PMAL.
• Opposite letters: A ↔ Z, B ↔ Y, and so on. The two positions always add up to 27: G (7) ↔ T (20).
• Two steps: BOX → YPC means shift +1 (CPY) and then reverse (YPC). Do the steps in the same order for the new word.

Number codes

• Positions: BED → 2-5-4, because B is 2, E is 5 and D is 4.
• Sums: a word's value can be the total of its positions: CAB = 3 + 1 + 2 = 6.
• Digit rules: "replace each digit by 9 minus the digit" turns 2047 into 7952.

Word codes

You may see several phrases with their codes, in mixed order. Find a word that appears in two phrases and look for the one code word that appears in both codes. Then remove the words you have solved. For "blue car park = ki lo ma" and "red car wash = ta ki su", the shared word "car" must be the shared code "ki".

Rules and exceptions

Workplace tests often give a policy and ask which case meets it. Break the policy into parts and check each case against every part.

• And means every condition is needed. Or means one is enough.
• Over 40 does not include 40. 40 or more does. Under $500 does not include $500.
• An exception overrides the general rule, but only for the cases it names.
• A time window such as "8 a.m. to 6 p.m., Monday to Friday" has two parts: the day and the time. Both must match.

Example: "Items can be returned within 30 days with a receipt. Sale items cannot be returned. Exception: damaged items can be returned within 30 days, even without a receipt and even if on sale." A damaged sale item with no receipt, returned after 12 days, can be returned, because the exception overrides the other rules.

Quiz thématique 5 : Codes, rules and exceptions

Lesson 6: Inductive patterns in words and tables

Inductive questions show you examples and ask you to find the rule. The examples may be a table, a set of inputs and outputs, a grid described in words, or a list of codes.

Rules in tables

Look along each full row and ask how the first numbers make the last one. Try adding, subtracting, multiplying, squaring, and two-step rules such as "subtract, then double". The same rule must work for every full row before you use it on the row with the question mark.

• 4, 6, 10 and 7, 8, 15: the third number is the sum.
• 3, 4, 12 and 5, 6, 30: the third number is the product.
• 2, 4, 8 and 3, 9, 27: a number, its square and its cube.
• 9, 4, 10 and 12, 5, 14: subtract, then double.

In a table where different rows belong to different people or items, each row can have its own rule. Do not mix them up.

Grids

• Each letter once: if every row and column holds A, B and C once, the missing letter is the one not yet in that row and column.
• Equal totals: if every row and column adds to the same total, find the total from a full row, then subtract.
• Grids described in words: look for what changes across a row (the count goes up by 1) and what stays the same (the shape).

Input-output rules

A rule that turns 2 into 7, 5 into 16 and 10 into 31 is "× 3, then + 1". Test simple guesses on the first pair, then confirm with the others. Squares are common too: 3 → 10, 6 → 37 is "square, then add 1".

Repeating patterns and days

For a pattern that repeats every 4 items, divide the position by 4 and use the remainder: the 37th item has remainder 1 (37 = 9 × 4 + 1), so it matches the 1st item. A remainder of 0 means the last item in the pattern. For days of the week, divide by 7: 15 days after a Monday is 2 weeks and 1 day, so it is a Tuesday. The 4th event in a series is only 3 gaps after the first.

Rules for codes, IDs and odd ones out

Compare examples part by part. In CAT3, HOUSE5 and DOOR4, the number is the count of letters. For an ID like CH19-4 for Lee Chan, hired in 2019, department 4, match each part to a fact. To find the odd one out, find a rule that fits all but one item: ACE, BDF and GIK skip one letter each time, but LMN does not.

Quiz thématique 6 : Inductive patterns in words and tables