Mathematical Reasoning Mock Test 18: 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

  • Time & Calendars: Duration, timetables, and date arithmetic.
  • Speed, Distance, Time: Applying S=D×T and unit consistency.
  • Unit Conversions: Consistent units within metric and mixed measures.
  • Inverse Operations: Working backwards from a result to find an unknown.
  • Multi-step Word Problems: Breaking down scenarios into equations and checking reasonableness.
  • Ratios: Part-part and part-whole relationships in applied settings.

Sample Questions from Test 18

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

Mathematical Reasoning

A sports centre offers three activities. The table shows which months each activity is available.

Question 1 · Multiple choice

Question

A sports centre offers three activities. The table shows which months each activity is available.

ActivityJanFebMarAprMayJunJulAugSepOctNovDec
Swimming✓✓✓✓✓✓✓✓✓✓✓✓
Tennis✓✓✓✓✓✓✓
Yoga✓✓✓✓✓

Options

Which of the following statements is/are correct?

Statement 1: There are 7 months when all three activities are available.

Statement 2: There is no month when only yoga is available without tennis also being available.

Statement 3: There are exactly 5 months when only swimming is available.

  • A.none of them
  • B.statement 1 only
  • C.statement 3 only
  • D.statements 1 and 2 only
  • E.statements 2 and 3 only

Correct answer

E.statements 2 and 3 only

Explanation

Read the table and list the months for each activity:

  • Swimming: all 12 months (Jan–Dec)
  • Tennis: Mar, Apr, May, Jun, Jul, Aug, Sep → 7 months
  • Yoga: Apr, May, Jun, Jul, Aug → 5 months

Check Statement 1: "7 months when ALL THREE are available"

All three are available only when swimming, tennis AND yoga all have a ✓.

Yoga months (Apr–Aug) are the most restricted. Swimming ✓ every month. Tennis ✓ from Mar–Sep.

So all three overlap only in Apr, May, Jun, Jul, Aug = 5 months (not 7).

Statement 1 is FALSE ✗

Check Statement 2: "No month when only yoga (without tennis)"

Yoga months: Apr, May, Jun, Jul, Aug. Tennis months: Mar, Apr, May, Jun, Jul, Aug, Sep.

Is every yoga month also a tennis month?

Apr–Aug are all within Mar–Sep. ✓

So every yoga month also has tennis — you can never have yoga without tennis. Statement 2 is TRUE ✓

Check Statement 3: "Exactly 5 months when only swimming"

"Only swimming" means swimming ✓ but tennis ✗ and yoga ✗.

Tennis is NOT available: Jan, Feb, Oct, Nov, Dec (5 months). In those 5 months, yoga is also not available (yoga ⊂ tennis months).

So only swimming is available in: Jan, Feb, Oct, Nov, Dec = 5 months ✓

Statement 3 is TRUE ✓

Answer: statements 2 and 3 only

Repeatable method for table-statement questions

  1. From the table, list which months/days each item appears.

  2. For each statement, translate it into a counting or comparison task.

  3. Check each statement individually — don't assume.

  4. Match the pattern of true statements to the correct answer option.

Mathematical Reasoning

Sam writes down the number 35. He reverses the digits to make the number 53. He then works out that 53 is 18 …

Question 2 · Multiple choice

Question

Sam writes down the number 35. He reverses the digits to make the number 53. He then works out that 53 is 18 more than his starting number, 35.

Lena writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number.

Options

What was the first digit of Lena's starting number?

  • A.2
  • B.3
  • C.8
  • D.1
  • E.9

Correct answer

D.1

Explanation

Step 1 — Understand the pattern using Sam's example

Sam's number: 35 → reversed: 53

Let's see why the difference is 18:

  • 35 = 3 × 10 + 5 (tens digit = 3, units digit = 5)
  • 53 = 5 × 10 + 3 (swapped)
  • 53 − 35 = 18

This always equals 9 × (units digit − tens digit): 9 × (5 − 3) = 9 × 2 = 18 ✓

Step 2 — Apply the formula to Lena's number

Let Lena's number = 10a + b (where a = tens digit, b = units digit).

Reversed number = 10b + a.

Reversed − Original = (10b + a) − (10a + b) = 9(b − a)

Lena's difference = 72:

9(b − a) = 72 b − a = 8

Step 3 — Find a and b (both single digits, a ≥ 1, b ≤ 9)

We need b = a + 8, both in range 1–9.

ab = a + 8Valid?
19✓ (both single digits, a ≥ 1)
210✗ (b = 10 is not a single digit)

Only one valid solution: Lena's number is 19.

Reversed = 91. Check: 91 − 19 = 72 ✓

Step 4 — Answer the question

The first digit (tens digit) of 19 is 1.

Answer: 1

Why 9 is a trap

9 is the LAST digit of Lena's number. The question asks for the FIRST digit. Read the question carefully!

Repeatable formula for any 2-digit reversed-digit problem

Reversed − Original = 9 × (units digit − tens digit)

If reversed > original: units digit > tens digit. If reversed < original: tens digit > units digit.

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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