Why shouldn’t you look only for the next number?
FNEGE describes, among other things, an intersection of number sets based on shared criteria. This Upsilar workshop practices the mechanism using two sets per exercise. These examples do not cover every type of logic question on the test.
In a sequence-completion problem, you may look for how to get from one term to the next. In a categorization problem, the question is different: what property do these numbers share? Irregular gaps do not prevent numbers from sharing a divisibility rule, number type, or digit property.
Examine one family of properties at a time: parity and divisibility, perfect squares, digit sums, position, or repeated digits. These are teaching prompts, not an official taxonomy. As soon as a rule fails for one item, discard or revise it before looking at the answer choices.
How can you combine divisibility and digit sums?
The numbers in a set do not need to be consecutive. Look for what they share, then apply both criteria to the same candidate.
Série A : 12, 20, 28, 44. Série B : 18, 27, 54, 63. Parmi les propositions, quel nombre satisfait à la fois les propriétés simples retenues pour A et B ?
Choose an answer.
The solution, step by step
36, using the criteria “multiple of 4” and “digit sum equals 9.”
The method in action
- Every number in A is a multiple of 4: 3 × 4, 5 × 4, 7 × 4, and 11 × 4. Every number in B has a digit sum of 9.
- 36 is divisible by 4, and 3 + 6 = 9. It satisfies both criteria.
- 24 and 52 are divisible by 4, but their digits do not add up to 9. 45 and 63 have a digit sum of 9, but are not divisible by 4.
How can you eliminate an appealing but incomplete rule?
The second exercise includes an even number in a set of squares. It checks whether your hypothesis covers the whole set, not just its last few elements.
Série A : 16, 25, 49, 81. Série B : 14, 21, 35, 56. Quel nombre satisfait à la fois les critères communs simples retenus pour chacune de ces deux séries ?
Choose an answer.
The solution, step by step
49.
The method in action
- The numbers in A are the squares of 4, 5, 7, and 9. The numbers in B are multiples of 7: 2 × 7, 3 × 7, 5 × 7, and 8 × 7.
- 49 = 7² is both a perfect square and a multiple of 7. 36 and 64 are squares but not multiples of 7; 28 and 42 are multiples of 7 but not squares.
- The rule “odd numbers” fails immediately for 16 in A. The rule “add 7” fails between 21 and 35 in B: a category does not require a constant difference.
The pitfall
Forcing a rule to justify an answer
A finite set can be described by many artificial rules. It would be misleading to claim that a short set mathematically dictates only one imaginable rule. These exercises use simple criteria that fit every example and distinguish the answer choices.
If two candidates remain, first check your second criterion and every number’s details. Do not add an exception just to eliminate a candidate. A rule that changes after each number does not describe the set well and is difficult to verify.
How can you practice recognizing useful criteria?
Start with one family at a time: identify squares, test divisibility, then examine digits. Next, combine two families. For each exercise, write down both properties before selecting an answer. This record shows whether an error came from identifying a rule or combining them.
Finish by creating one candidate that satisfies only the first criterion and another that satisfies only the second. If you can explain why each fails, you understand the intersection. Then increase the variety of numbers instead of relying only on faster recognition.
Key takeaways
- A number category is not necessarily a sequence to continue.
- Check each property against every number.
- The final candidate must satisfy both criteria without an added exception.