11+ Verbal Reasoning: Numbers and Logic

The number puzzles in an 11+ paper reward one habit above all others: find the rule, then check it against everything you were given before you use it. Four sequences here work up from a steady step to a multiplier, to a step that grows by one each time, to a pair of rules taking turns, and in each case the way in is to write the gaps down rather than to stare at the numbers. Two more puzzles give a middle number made from the two on either side, with two worked examples to learn from — and the second pair deliberately uses a different rule from the first, so a child who assumes the rule carries over gets it wrong. Then the logic: a row of four children to be reconstructed from where two of them are not, four ages to be put in order with the question asking for the second youngest rather than the youngest, a count of forty-five days from a Wednesday, and finally two facts about pencils in a tin with four statements, only one of which the facts actually force. That last one is the whole skill in miniature: for each statement, try to imagine the facts being true and the statement being false. If you can, it is not the answer. Zestly is an independent study tool. It is not affiliated with any exam board and it is not an exam centre.

  • Find the rule of a sequence by writing down the gap between every pair, not just the first two
  • Handle sequences that multiply, whose step grows, and where two rules take turns
  • Work out how a middle number is made from two outside ones, testing the rule on both worked examples
  • Expect the rule to change between one puzzle and the next rather than carrying it over
  • Reconstruct an order from clues about where people are and are not
  • Count days forward by dividing by seven and using the remainder
  • Tell what a set of facts forces from what it merely allows

All the pencils in the tin are red. Some of the red things in the room are pencils. Which statement must be true? — Every pencil in the tin is red. The test to apply is whether you can imagine the facts being true and the statement being false at the same time.

Sample question

All the pencils in the tin are red. Some of the red things in the room are pencils. Which one of these statements must be true?

See the answer

Every pencil in the tin is red.

In a question like this, only what the facts force you to accept counts. The first fact says every pencil in the tin is red, so the correct statement is simply that fact said again, and nothing can make it false. The statement that every red thing in the room is a pencil turns the second fact round the wrong way: some of the red things being pencils leaves the rest of them free to be anything at all. The statement about blue pencils goes outside the tin, and the facts say nothing whatever about pencils elsewhere in the room. And the statement that the tin holds nothing but pencils adds something too: being told the pencils in it are red does not tell you that there is not also a rubber or a ruler in there. The test to apply is whether you can imagine the facts being true and the statement being false at the same time.

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← 11+ Verbal Reasoning

↑ 11+ and KS2 SATs

Key Stage 2 SATs are set by the Standards and Testing Agency (Department for Education); 11+ examinations are set by individual schools, local authorities and providers such as GL Assessment. Zestly is not affiliated with or endorsed by any of them. These materials are our own and reproduce no official paper.