Thinking Skills Mock Test 3: 2027 NSW Selective Format

Step 1 — Understand the shading rule.

A cell is shaded when row × column = even number.

A product is even whenever AT LEAST ONE of the factors is even. The ONLY way to get an odd product is if BOTH the row AND column numbers are odd.

Step 2 — Find the unshaded cells (both odd).

In a 5×5 grid:

• Odd rows: 1, 3, 5 → 3 rows
• Odd columns: 1, 3, 5 → 3 columns

Unshaded cells = 3 × 3 = 9 cells (every combination of odd row and odd column)

Step 3 — Visualise the grid (■ = shaded, □ = unshaded).

     Col1  Col2  Col3  Col4  Col5
Row1: □     ■     □     ■     □
Row2: ■     ■     ■     ■     ■
Row3: □     ■     □     ■     □
Row4: ■     ■     ■     ■     ■
Row5: □     ■     □     ■     □

The 9 unshaded squares (□) appear at the odd-odd intersections. Everything else is shaded.

Step 4 — Count shaded cells.

Total cells = 5 × 5 = 25

Shaded cells = 25 − 9 = 16

Answer: 16

Step 1 — Rotate the net to see face relationships clearly.

Step 2 — Identify opposite faces by folding.

Using the colour coding:

• 🟢 Two diamond faces are opposite each other.
• 🔵 Hexagon and arrow are opposite each other.
• 🩷 Dotted-line face and hatched circle are opposite each other.

Step 3 — Confirm opposite pairs with coloured arcs on the net.

Since opposite faces cannot be seen in the same 3D view, we can eliminate options that show any opposite pair together:

• Option C: Shows the dotted-line face and the upward arrow in the same view. But dotted line and arrow are on opposite faces — impossible. ❌ Eliminated.

• Option A: Shows the dotted-line face with the pointed end of the diamond facing toward it. On the rotated net, the dotted line faces the flat side of the diamond, not the pointy end. ❌ Eliminated.

• Option D: Shows the upward arrow pointing toward the hatched circle. On the net, the arrow points away from the circle (they are in opposite directions in the column). ❌ Eliminated.

By elimination, the only remaining option is B, which correctly shows the hexagon and diamond on adjacent faces with consistent orientation.

The answer is B.