Critical thinking and problem solving: the stage 2 problems
Updated: 7 October 2026
This stage tests thinking rather than a textbook formula: reading data, comparing, finding the pattern and drawing a conclusion. The problems are mathematical, but the solution is usually reasoning, not arithmetic.
What is the test like?
- 40 questions; the 2025 announcements gave 90 minutes.
- Within maths, but mostly in words or pictures: tables, charts, shapes.
- Multiple choice; no written solution, but rough paper is needed.
- On the same day as English, as the first part of stage 2.
Problem types
- Patterns: find the next term in a sequence of numbers or shapes.
- Logic grids: who wears which colour, who sits where, deduced from several clues.
- Reading tables and charts: bar charts, finding the largest or smallest, working out a difference.
- Comparing and balancing: how many times heavier, equal weights.
- Counting and combinations: how many ways, how many pairs.
- Spatial reasoning: cube nets, mirror images, rotating a shape.
- Extra data: the problem includes a number that is not needed, and it has to be set aside.
How to solve them
- Put the clues in a table. Names as rows, attributes as columns; each clue fills or crosses out a cell.
- Mark what is known, state what is asked. What is given and what is wanted, as two separate lists.
- Test the options. Work backwards: put each answer into the problem and one survives.
- Check the answer against the problem. Does the number fit every clue? Only then mark it.
Worked examples
Continue the sequence: 2, 5, 11, 23, ?
- A35
- B44
- C47
- D46
Show the answer
Correct answer: C — 47
Each term is the previous one doubled plus 1: 2·2+1=5, 5·2+1=11, 11·2+1=23, 23·2+1=47. The differences (3, 6, 12) double too, which is the same rule.
Aziza, Bobur and Dilnoza took three different fruits: an apple, a pear and a banana, one each. Aziza did not take the banana. Bobur took neither the apple nor the banana. What did Dilnoza take?
- AThe apple
- BThe pear
- CThe banana
- DCannot be determined
Show the answer
Correct answer: C — The banana
Bobur took neither the apple nor the banana, so Bobur has the pear. Aziza did not take the banana and the pear is Bobur's, so Aziza has the apple. The remaining banana is Dilnoza's.
One watermelon weighs the same as two melons, and one melon weighs the same as three apples. How many apples weigh the same as two watermelons?
- A6
- B8
- C12
- D24
Show the answer
Correct answer: C — 12
One watermelon = 2 melons = 2·3 = 6 apples. Two watermelons = 6·2 = 12 apples. The wrong answer 6 is for one watermelon; 24 multiplies once too often.
How to practise
Two or three problems a day, timed, with the solution explained aloud. If the child can answer why, the problem is learned; finding the answer without being able to explain it is not there yet.
Prezi Prep has a critical-thinking section: timed problem sets in the stage-two format. Logic and pattern problems also appear inside the maths tests.
Questions and answers
Start preparing today
Topic tests, weekly mock exams and English words, for year 4, in the entrance-exam format. The free plan never expires.
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