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TARA Problem Solving Book: Hard Edition

Sharpen TARA problem solving across fractions, time and calendar questions, spatial reasoning and algorithm and workflow reasoning. Explore the course book.

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About this book

This book prepares students for the problem solving section of the TARA admissions test. It is a hard edition built around 15 core topics plus algorithm and workflow reasoning, aimed at students who want to practise beyond the most straightforward questions.

The topics start with number skills such as fractions, percentages, place value and the four operations, including a dedicated section on the order-of-operations trap. It then covers mean and average, money problems, time and calendar questions, measures and unit conversion, area and perimeter, and the volume of boxes.

Later sections focus on reading tables, graphs and charts, multi-step numerical reasoning, spatial reasoning and practical problem solving, followed by algorithm and workflow reasoning. A diagram appendix explains how to use the visuals, and the book closes with a revision section.

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Sample · 01-TARA Problem Solving Book · 15 Topics + Algorithm & Workflow · Hard Edition

Chapter 1 Overview

TARA Problem Solving Book · 15 Topics + Algorithm & Workflow · Hard Edition

This version restores the full TARA Problem Solving topic range and adds Algorithm and Workflow reasoning. The earlier version had too few topics; this edition has all requested topics with detailed explanations, diagrams and hard decision-making MCQs.

Book map

CoverageDesign
15 official-style Problem Solving topicsFractions through Practical Problem Solving
Additional Algorithm and Workflow topicConditional steps, loops, stop rules and process logic
Question levelHard TARA-style decision-making traps, not easy drills

Teacher guidance

For each topic, teach students to name the hidden structure before they calculate: original amount, remaining amount, group weight, unit, threshold, overlap, sample space, or workflow condition.

readmodeldecide

1 Fractions

1 Fractions

part of whole Hard fraction question Is the fraction of original, remaining, change, or final amount?
Use this diagram to teach denominator choice: original amount, remaining amount, and change are different bases.
part / wholeWhich whole?original, remainder, or change?

Detailed explanation

Fractions become hard when the reference whole changes. The key question is: does the fraction refer to the original amount, the amount left, the amount added, or the change between two states?

How to teach this topic

Start with a short modelling question: What is the input? What is the total? What is being compared? Which value changes? Which value stays fixed? This prevents fast but wrong arithmetic.

Question 1
A tank is \(\frac35\) full. After \(18\) litres are added, it is \(\frac45\) full. What is the tank capacity?
  • A60 L
  • B75 L
  • C90 L
  • D100 L
  • E120 L
Question 2
A student spends \(\frac14\) of her money, then \(\frac13\) of what remains. What fraction remains?
  • A\(\frac13\)
  • B\(\frac12\)
  • C\(\frac{5}{12}\)
  • D\(\frac{7}{12}\)
  • E\(\frac23\)
Question 3
Three-fifths of a class are girls. There are \(8\) more girls than boys. How many students are in the class?
  • A24
  • B32
  • C40
  • D48
  • E60
Question 4
A bottle is \(\frac78\) full. \(120\) ml is poured out and it becomes \(\frac58\) full. What is the capacity?
  • A360 ml
  • B420 ml
  • C480 ml
  • D540 ml
  • E600 ml

2 Percentages

2 Percentages

Original 100% Multiplier e.g. 0.75 or 1.20 Final divide to reverse
Reverse percentage questions are solved by dividing by the multiplier, not by subtracting the percentage from the final.
part / wholeWhich whole?original, remainder, or change?

Detailed explanation

Percentages are multipliers. Reverse percentages and repeated changes require multiplication or division by the correct multiplier, not adding and subtracting percentage points casually.

How to teach this topic

Start with a short modelling question: What is the input? What is the total? What is being compared? Which value changes? Which value stays fixed? This prevents fast but wrong arithmetic.

Question 5
After a \(25\%\) discount, a jacket costs \(£54\). What was the original price?
  • A£67.50
  • B£70
  • C£72
  • D£75
  • E£81
Question 6
A value is increased by \(20\%\), then decreased by \(20\%\). What is the net effect?
  • ANo change
  • B4% decrease
  • C4% increase
  • D20% decrease
  • E40% decrease
Question 7
Two groups have pass rates \(80\%\) of \(30\) students and \(60\%\) of \(70\) students. What is the overall pass rate?
  • A66%
  • B68%
  • C70%
  • D72%
  • E74%
Question 8
A shop gives \(15\%\) off, then \(10\%\) off the reduced price. What is the total discount?
  • A21.5%
  • B23.5%
  • C24%
  • D25%
  • E26.5%

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Built for TARA preparation

Topics follow the TARA syllabus with visual explanations and worked solutions close to the lesson content.

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