Which representation should you choose?
FNEGE describes explicit scenarios in the Critical Reasoning subtest that require finding a unique solution. Our exercises develop this skill with small constraint sets; they do not claim to establish how often this question type appears on the test.
For an ordering problem, draw numbered slots from left to right. For an assignment problem, make a table with people in rows and items in columns. For a conditional, draw an arrow. Each representation should show the relationship actually given without adding a property.
“Ana passe avant Bruno” (Ana presents before Bruno) allows zero, one, or more positions between them. “Chloé passe immédiatement après Bruno” (Chloé presents immediately after Bruno) instead creates a Bruno–Chloé block. The second constraint limits the possible positions more, so start there. Then keep the question in mind; you do not always need a unique full ordering.
How can you prove a position is required?
Starting diagram: [1] [2] [3] [4]. Place the Bruno–Chloé block in these four slots, then eliminate positions that conflict with the other statements.
| Case | Position 1 | Position 2 | Position 3 | Position 4 |
|---|---|---|---|---|
| Block in slots 2–3 | Ana | Bruno | Chloé | Daria |
| Block in slots 3–4 | Ana | Daria | Bruno | Chloé |
Ana, Bruno, Chloé et Daria présentent chacun une fois, à quatre places successives. Ana passe avant Bruno. Chloé passe immédiatement après Bruno. Daria ne passe pas en premier. Qui doit passer en premier ?
Choose an answer.
The solution, step by step
Ana.
The method in action
- The Bruno–Chloé block cannot take slots 1–2 because Ana must come before Bruno. If it takes slots 2–3, Ana is in slot 1 and Daria is in slot 4.
- If the block takes slots 3–4, Ana and Daria take slots 1–2. Since Daria cannot go first, Ana is again in slot 1.
- The two possible orders are Ana–Bruno–Chloé–Daria and Ana–Daria–Bruno–Chloé. The full order is not unique, but the first position is. The last answer choice is therefore false.
How can you propagate a definite assignment?
When each person receives exactly one item and each item is assigned only once, an assignment eliminates one row and one column of possibilities. This elimination depends on the words “exactly” and “only once”; without them, the table does not follow the same rule.
Léa, Sam et Noé reçoivent chacun un badge de couleur différente : rouge, bleu ou vert. Léa n’a pas le rouge. Sam n’a pas le bleu. Noé a le bleu. Quelle attribution est nécessaire ?
Choose an answer.
The solution, step by step
Sam gets red.
The method in action
- Noé has blue, leaving red and green for Léa and Sam. Léa cannot take red, so she gets green.
- Sam therefore gets red. The constraint “Sam does not have blue” is consistent but adds nothing once Noé’s badge is fixed.
- The other choices violate either an explicit exclusion or the rule that each color is assigned only once. Redundant information is not a contradiction.
The pitfall
Confusing a possible example with a required consequence
A valid ordering proves only that it is possible. To claim that someone must always be second, you must eliminate cases in which they are not. In the first exercise, Bruno is second in one case and third in another: both positions are possible, so neither is required.
The wording of the question determines what you need to do. “Could be true” asks for a compatible example; “must be true” asks for a property shared by all cases. After choosing, check the key verb in the prompt one more time.
How can you test an implication without reversing it?
The rule “if X, then Y” rules out X without Y. It does not rule out Y without X; the arrow cannot automatically be reversed.
Un comité choisit exactement deux projets parmi X, Y et Z. S’il choisit X, il doit aussi choisir Y. Quel projet doit nécessairement être retenu ?
Choose an answer.
The solution, step by step
Y.
The method in action
- Before applying the constraint, the possible pairs are XY, XZ, and YZ. The rule excludes XZ because it includes X without Y.
- That leaves XY and YZ. Y appears in both; X and Z each appear in only one case.
- Selecting Y does not require X; the YZ pair is still allowed. Reversing the arrow would remove that case without justification and create false certainty.
Key takeaways
- Represent order, adjacency, and exclusion with distinct symbols.
- Build cases starting with the most restrictive constraints.
- A necessary condition must hold in every valid case.