Sample Questions from Test 11

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

Mathematical Reasoning

A farm had 348 white rabbits and grey rabbits altogether. After 102 white rabbits are sold, the remaining whi…

Question 1 · Multiple choice

Question

A farm had 348 white rabbits and grey rabbits altogether. After 102 white rabbits are sold, the remaining white rabbits are as many as the grey rabbits. How many white rabbits and grey rabbits were there at first?

Options

A. $200 white and 148 grey$
B. $225 white and 123 grey$
C. $230 white and 118 grey$
D. $210 white and 138 grey$
E. $220 white and 128 grey$

Correct answer

B.

225 white and 123 grey

Explanation

Step 1: Set up the equations Let w = number of white rabbits at first, and g = number of grey rabbits at first. Equation 1 — total rabbits: w + g = 348 After selling 102 white rabbits, the remaining white rabbits equal the grey rabbits: Equation 2: w - 102 = g Step 2: Substitute and solve From Equation 2: g = w - 102 Substitute into Equation 1: w + (w - 102) = 348 2w - 102 = 348 2w = 348 + 102 = 450 w = 450 \div 2 = 225 white rabbits g = 348 - 225 = 123 grey rabbits Check: After selling 102 white: 225 - 102 = 123 = grey rabbits ✓ Answer: 225 white rabbits and 123 grey rabbits Option White Grey Sum After selling 102 A 200148348 98\neq148 ✗ B 225123348 123=123 ✓ C 230118348 128\neq118 ✗ D 210138348 108\neq138 ✗ E 220128348 118\neq128 ✗

Mathematical Reasoning

A school auditorium has 12 cement pillars. They are each 3 decimetres long, 2 decimetres wide and 5 metres hi…

Question 2 · Multiple choice

Question

A school auditorium has 12 cement pillars. They are each 3 decimetres long, 2 decimetres wide and 5 metres high. The surface of these pillars needs to be painted. How many square metres is the total area to be painted?

Options

A. $60 m²$
B. $66 m²$
C. $72 m²$
D. $78 m²$
E. $50 m²$

Correct answer

A.

60 m²

Explanation

Step 1: Convert units to metres The pillar dimensions mix decimetres and metres: Length = 3 decimetres = 0.3 m (1 dm = 0.1 m) Width = 2 decimetres = 0.2 m Height = 5 m (already in metres) Step 2: Identify what needs to be painted Only the four side faces (lateral surface) of each pillar are painted — the bottom is on the floor and the top is against the ceiling. Step 3: Find the perimeter of one pillar's cross-section Each pillar is rectangular with dimensions 0.3 m \times 0.2 m. Perimeter = 2 \times (length + width) = 2 \times (0.3 + 0.2) = 2 \times 0.5 = 1 m Step 4: Find the painted area per pillar Lateral area = perimeter \times height = 1 \times 5 = 5 m² per pillar Step 5: Find the total for all 12 pillars Total = 12 \times 5 = 60 m² Answer: 60 m² Option Value Why it is wrong A 60 m² 12\times2(0.3+0.2)\times5=60. ✓ B 66 m² Added top/bottom of some pillars. ✗ C 72 m² Used dimensions in dm without converting. ✗ D 78 m² Included all 6 faces per pillar. ✗ E 50 m² Used only 10 pillars: 10\times5=50. ✗

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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Mathematical Reasoning Mock Test 11: 2027 NSW Selective Format

Skills Covered in this Test

Sample Questions from Test 11

Core Competencies

Prepare with Precision

Option	White	Grey	Sum	After selling 102
A	200	148	348	98≠148	✗
B	225	123	348	123=123	✓
C	230	118	348	128≠118	✗
D	210	138	348	108≠138	✗
E	220	128	348	118≠128	✗

Option	Value	Why it is wrong
A	60 m²	12×2(0.3+0.2)×5=60. ✓
B	66 m²	Added top/bottom of some pillars. ✗
C	72 m²	Used dimensions in dm without converting. ✗
D	78 m²	Included all 6 faces per pillar. ✗
E	50 m²	Used only 10 pillars: 10×5=50. ✗