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Multi-step problems

Multi-step problems chain several skills (fractions, percentages, ratio, algebra) into one question. They are common in the harder Stage 1 questions and in written Stage 2 papers. Break the problem into small, labelled steps.

What is tested

  • Combining fractions, percentages and ratio in one problem
  • Working out what to find first
  • Forming and solving equations from a description

Worked example

Tom has £50. He spends 2/5 on a book, then 25% of what is left on a snack. How much does he have now?

  1. Book: 2/5 of 50 = £20, leaving £30.
  2. Snack: 25% of 30 = £7.50.
  3. Left: 30 − 7.50 = £22.50.

Answer: £22.50

Exam-day checklist

  • Underline what you are asked to find, then list what you need first.
  • Do one step per line and label it.
  • Watch for 'of what is left' versus 'of the original'.
  • Check the answer against the story.

Common mistakes

  • Taking the second percentage from the original amount.
  • Skipping a step - on a written paper this can lose method marks.
  • Answering an intermediate value.

Try it yourself

1. A shop has 60 apples. 1/3 are sold in the morning and 1/4 of the rest in the afternoon. How many are left?

Show answer

30

Morning: 20 sold, 40 left. Afternoon: 1/4 of 40 = 10 sold, so 30 left.

2. Ali is three times as old as Ben. In 4 years their ages add to 32. How old is Ben now?

Show answer

6

Now they total 32 − 8 = 24, which is 4 parts (3 + 1), so Ben = 6 and Ali = 18.

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More topic guides

Ratio and proportionPercentages, fractions and decimalsAlgebra: equations and sequencesProbabilityVerbal reasoning: codesVerbal reasoning: logic and orderingNon-verbal reasoning: sequences and matricesEnglish: inference and comprehensionArithmeticNumber and place valueFractionsDecimalsProportionNumber sequencesGeometry: angles and shapesMeasurementTimeMoneyAveragesData handlingWorded problems3D shapes: volume and surface areaCoordinates and translationsSpeed, distance and timeVenn and Carroll diagramsEnglish: grammarEnglish: spellingEnglish: punctuationEnglish: vocabularyEnglish: editing and proofreadingEnglish: comprehensionEnglish: comparing two textsEnglish: paragraph ordering and cohesionEnglish: register and purposeEnglish: deductionEnglish: sentence completionEnglish: contextEnglish: word relationshipsEnglish: literary understandingEnglish: creative writingShuffled sentencesClauses: main, subordinate and relativeVerbal reasoning: analogiesVerbal reasoning: classificationVerbal reasoning: letter and word sequencesVerbal reasoning: word relationshipsVerbal reasoning: hidden wordsVerbal reasoning: compound wordsVerbal reasoning: letter patternsMove a letterInsert a letterAnagrams and word laddersLetter and symbol sumsNon-verbal reasoning: transformationsNon-verbal reasoning: rotationsNon-verbal reasoning: reflectionsNon-verbal reasoning: symmetryNon-verbal reasoning: spatial reasoningNon-verbal reasoning: analogiesNon-verbal reasoning: paper foldingNon-verbal reasoning: cube netsNon-verbal reasoning: odd one outPlans and elevations (3D views)Shape assemblyTime management in the examEliminating incorrect optionsIdentifying distractorsChecking your workReading questions carefullySkipping and returning to questionsWorking under pressureHandling unfamiliar questions

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