Mathematical Reasoning Mock Test 3: 2027 NSW Selective Format

Build fluency with multi-step problems, diagrams, and data interpretation in our 35-question mock test—aligned to the Janison-style NSW Selective Mathematical Reasoning paper.

Duration

40 Minutes

Format

2027 NSW Format

Questions

35 multiple-choice

Level

Official Selective Test Level

Skills Covered in this Test

This mock test mirrors the official weightings of the NSW Department of Education exam.

The breakdown

  • Graph Interpretation: Reading scales, trends, and values from charts and tables.
  • Ratios: Part-part and part-whole relationships in applied settings.
  • Percentages: Discounts, changes, and comparisons expressed as percent.
  • Mean, Median & Mode: Choosing and computing the right average for the data.
  • Venn Diagrams: Overlaps, unions, and logical counts from sets.
  • Logical Deduction: Using given constraints to eliminate impossible answers.

Sample Questions from Test 3

The first two questions of this mock test (same order and wording as the timed exam).

Mathematical Reasoning

You are given two numbers, 5976 and 1432. Subtract 4 from the first number and add 4 to the second number. Af…

Question 1 · Multiple choice

Question

You are given two numbers, 5976 and 1432. Subtract 4 from the first number and add 4 to the second number. After how many repeats of this operation would they become equal?

Options

  • A.284
  • B.1136
  • C.568
  • D.540
  • E.454

Correct answer

C.568

Explanation

Step 1: Find the starting gap between the two numbers

Starting gap = 5 976 − 1 432 = 4 544

Step 2: Find how much the gap closes each repeat

Each repeat:

  • First number decreases by 4
  • Second number increases by 4

Gap closes by 4 + 4 = 8 per repeat

Step 3: Find the number of repeats

Repeats needed = Starting gap ÷ Closing rate per repeat

= 4 544 ÷ 8 = 568

Check:

After 568 repeats:

5 976 − (4 × 568) = 5 976 − 2 272 = 3 704

1 432 + (4 × 568) = 1 432 + 2 272 = 3 704 ✓

Both numbers equal 3 704 after 568 repeats.

Answer: 568 repeats

Mathematical Reasoning

Mr Smith made 81 spare parts in 3 hours. Jack made 24 spare parts in 1 hour. How many spare parts did Mr Smit…

Question 2 · Multiple choice

Question

Mr Smith made 81 spare parts in 3 hours. Jack made 24 spare parts in 1 hour. How many spare parts did Mr Smith and Jack make in 1 hour in total?

Options

  • A.27
  • B.51
  • C.81
  • D.48
  • E.24

Correct answer

B.51

Explanation

Step 1: Find Mr Smith's rate per hour

Mr Smith made 81 spare parts in 3 hours.

Mr Smith's rate = 81 ÷ 3 = 27 parts per hour

Step 2: Add both rates

WorkerRate (parts/hour)
Mr Smith27
Jack24
Total51

Answer: Together they make 51 spare parts in 1 hour

Core Competencies

3D NetsAlgebraic SubstitutionsAngle PropertiesArea & PerimeterCartesian CoordinatesDecimalsFractionsGraph InterpretationInverse OperationsLogical DeductionMean, Median & ModeMental ArithmeticMulti-step Word ProblemsNumber SequencesOrder of OperationsPercentagesPrime NumbersProbability LogicProfit & LossRatiosReflection & RotationSpeed, Distance, TimeSquare & Cube NumbersSymmetryTime & CalendarsUnit ConversionsVenn DiagramsVolume & Capacity

Prepare with Precision

  • Sharpen accuracy on multi-step and diagram-based items.
  • Get comfortable with the Janison-style interface.
  • Identify topics to revisit before exam day.

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