11 plus Classification & Logic questions

What a Classification & Logic question looks like

Classification & Logic is the part of 11 plus maths where several rules apply at once. A question states two, three or four conditions, gives five options, and exactly one option meets all of them. That stacking separates it from Number Properties, which asks about one property at a time, and from Venn Diagrams, which is about reading the regions of a diagram already filled in.

The rules come from a short, familiar list. Most of these questions work with number properties: multiples and factors, primes, square numbers, cube numbers, triangular numbers, odd and even, how many digits a number has, what its digits add up to, and whether it sits between two limits. About a fifth work with flat shapes instead: sides, parallel sides, right angles, and whether all the sides and corners match.

The name is broader than the questions are. There are no syllogisms, no if-then chains and no puzzles about who owns which pet, and a child never sorts a set into groups: the answer is always one of five options. Logic here means holding a checklist and refusing to stop early.

Three smaller variations sit alongside the main one: naming the property that three alike numbers share, supplying the missing row labels for a set already sorted into a small table, and deciding which of three children’s claims about numbers are wrong. About one question in six draws the two groups as overlapping circles, or lays them out as a table, but that changes nothing about the method.

Example one: Priya’s number

Priya says: “My number is a two-digit number, a square number, and an odd number.” Which number could she mean? The options are 49, 16, 64, 36 and 9.

Take the rules in the order that shrinks the list fastest. Two-digit square numbers are 16, 25, 36, 49, 64 and 81. Apply the odd rule and 25, 49 and 81 survive. Only 49 is among the options, so the answer is 49.

The option that catches careful children is 9. It is a square number, 3 times 3, and it is odd, so it passes two rules out of three. It fails the rule easiest to read past, because two-digit does not sound like a rule at all.

Example two: the shape that is regular

Which shape satisfies all of these: it is a polygon, it has exactly 5 sides, all the angles inside it are equal, and all its sides are equal? The options are regular hexagon, irregular pentagon, hexagon, regular octagon and regular pentagon.

Two words do most of the work here, exactly and regular. Exactly 5 sides means a pentagon, so both hexagons and the octagon go whatever else is true of them, leaving the irregular pentagon and the regular pentagon. Regular is the word for a shape whose sides are all the same length and whose corners are all the same size, so the last two rules are the definition of regular. The answer is regular pentagon.

Irregular pentagon tempts because it passes the rule the eye reaches first: five sides, and pentagon is the word a child is hunting for.

Example three: which of them are wrong

Aisha says every number ending in 4 is a multiple of 4. Ben says every multiple of 6 is also a multiple of 3. Cal says all even numbers are multiples of 4. Which statement about them is true? Two of the five options are “Aisha and Ben are both wrong” and “Aisha and Cal are both wrong”.

To show a claim like this is wrong you need one number that breaks it, and one is enough. 14 ends in 4 and does not divide by 4, so Aisha is wrong. 6 is even and does not divide by 4, so Cal is wrong. Ben is different: no number breaks his claim, because every 6 is made of two 3s, so anything built out of sixes is built out of threes too. The answer is that Aisha and Cal are both wrong.

“Aisha and Ben are both wrong” is the trap. A child finds the number that breaks Aisha’s claim, feels the work is done, and assumes the next child named must be wrong too.

How to answer it

1. Write the rules out as a list before looking at the options. The question runs them together in one sentence, and the one that gets lost is the shortest, like “less than 60” or “two-digit”.
2. Start with the rule that removes the most options. Exactly five sides, or two digits, often leaves only two standing before any harder checking begins.
3. Test every option against every rule, ticking and crossing as you go. Stopping at the first option that passes a rule is the biggest single source of lost marks here.
4. Where a rule involves a list you already know, write it out: the two-digit square numbers, the factors of 60, the multiples of 7 below 60.
5. Read the winning option back against every rule before moving on.

Common mistakes

• Answering after one rule. Every wrong option passes at least one rule, so an early answer nearly always feels right. 9 is a square number and it is odd, and still wrong when the question asked for two digits.
• Missing the small rule. Greater than 10 rules out 9, and less than 20 rules out 20 itself. The word exactly decides more of these than the arithmetic does.
• Swapping factors and multiples. Asked for a number that is a factor of both 24 and 36, a child who reads factor as multiple has lost the question on the first line.
• Forgetting how the shape families overlap. Asked for a four-sided shape with a right angle that is not a rectangle, a child answers square, which the last rule excludes because a square is a special kind of rectangle.
• Assuming one claim is wrong because its neighbour is. Breaking the first claim says nothing about the second, and the options are built so the assumption has somewhere to land.

How to practise 11 plus Classification & Logic questions

Two things make these quicker, and they are worth practising separately. The first is instant recall of the lists the rules draw on: times tables, the square numbers to 144, the cube numbers, the primes below 30, and how to write out the factors of a number without missing any. The second is the checklist habit, which builds more easily out loud than on paper: read the question, say the rules back as a list, then say yes or no to each option in turn. 11+ Daily has a Classification & Logic project covering the number rules, the shape rules and the false-claim variation, and it sits with the rest of 11 plus maths practice so the habit keeps being used across the eleven plus year. Every question is original to 11+ Daily, nothing is a past paper, nothing is licensed, and the bank is re-checked in rounds. We have also written about how much 11 plus practice a child needs each day.

Questions parents ask