What does each letter mean?
The grid below follows the FNEGE candidate booklet reviewed on October 15, 2026. The order matters: C means the statements must be combined, while D means each statement is sufficient on its own. The problems below are educational exercises by Upsilar.
| Answer | Decision |
|---|---|
| A | (1) alone is sufficient; (2) alone is not. |
| B | (2) alone is sufficient; (1) alone is not. |
| C | Neither is sufficient alone; together they are. |
| D | Each is sufficient on its own. |
| E | Even together, they are not sufficient. |
What does a contaminated analysis look like?
Create three areas on your scratch paper: “original information,” “(1) alone,” and “(2) alone.” The original information can be used in every area. A value obtained from (1), however, cannot carry over into the (2) area. You must redo the reasoning using only the information allowed there.
If the first statement yields a simple number, do not reuse it to test the second. Start over with the prompt and (2), then look for two situations compatible with only that information. If they produce different answers to the question, (2) is insufficient.
Un rectangle a des côtés strictement positifs L et l. Quelle est son aire ? (1) Son périmètre vaut 30 cm. (2) Sa longueur L vaut 10 cm.
Choose an answer.
The solution, step by step
C.
The method in action
- With (1) alone, L + l = 15. The pairs (10, 5) and (9, 6) give different areas: 50 and 54. The first statement is insufficient.
- With (2) alone, L = 10, but l is still unrestricted: 5 or 6 would give an area of 50 or 60. Reusing L + l = 15 here would contaminate the analysis with information from (1).
- Together, the statements require l = 5 and give a unique area of 50 cm². C is correct. D would be the incorrect conclusion from analyzing both statements together each time.
The pitfall
Confusing “the answer is no” with “it is impossible to know”
If the question asks “Is x greater than 5?”, a statement that requires x = 2 is sufficient: the answer is no, but it is certain. Information is insufficient when two allowed values produce different answers, such as x = 2 and x = 8.
You do not necessarily need to find the exact value of every unknown. An entire range may be enough to decide yes or no. The answer to the question must be unique; the intermediate values do not all have to be.
Can an inequality be sufficient on its own?
Read strict inequalities carefully. Being greater than or equal to a bound does not always give the same answer as being strictly greater.
x est un nombre réel. Est-il strictement supérieur à 5 ? (1) x < 4. (2) x = 3.
Choose an answer.
The solution, step by step
D.
The method in action
- With (1), all allowed values are less than 4 and therefore less than 5. The answer is always no, so (1) is sufficient.
- With (2), x is 3 and the answer is also no, so (2) is independently sufficient.
- D means each statement is sufficient on its own. C would be incorrect because combining them is unnecessary; E would confuse a negative answer with not knowing.
What counterexample should you construct?
A good counterexample satisfies all the information allowed in that step. To test the combination, it must satisfy (1) and (2) at the same time. Two examples with the same result do not prove sufficiency; two different results are enough to prove insufficiency.
x et y sont strictement positifs. Quelle est leur somme ? (1) xy = 24. (2) x > y.
Choose an answer.
The solution, step by step
E.
The method in action
- (1) alone allows (6, 4), with a sum of 10, and (8, 3), with a sum of 11. It is insufficient. (2) alone obviously leaves many possible pairs.
- Both pairs (6, 4) and (8, 3) also satisfy x > y; even together, the statements do not determine the sum.
- C may seem tempting because two statements appear to provide two constraints. But counting statements is no substitute for examining what they actually determine.
Key takeaways
- Keep the original information and isolate the additional statements.
- A definite “no” is just as sufficient as a definite “yes.”
- To prove insufficiency, produce two different compatible answers.