Mathematical Reasoning Mock Test 17: 2027 NSW Selective Format

The method: list every combination, then test each statement

Choose 3 different numbers from {2, 4, 7, 9}. There are exactly 4 ways to do this:

All possible totals: 13, 15, 18, 20

Statement 1: "The total is always greater than 12."

"Always" means: check every total — even one exception would make it false.

• 13 > 12 ✓, 15 > 12 ✓, 18 > 12 ✓, 20 > 12 ✓

Every total is greater than 12 → Statement 1 is TRUE ✓

Statement 2: "The total can be a multiple of 9."

"Can be" means: does at least one combination give a multiple of 9?

Multiples of 9: 9, 18, 27 …

18 appears in the list (from 2 + 7 + 9) → Statement 2 is TRUE ✓

Statement 3: "The total cannot be even."

"Cannot be even" means: none of the totals should be even. But:

18 and 20 are both even — so the total CAN be even → Statement 3 is FALSE ✗

Answer: statements 1 and 2 only

Repeatable checklist

1. Write ALL combinations (leave nothing out; use a system like "smallest first").

2. Calculate each sum.

3. "Always" → every single value must fit (one exception = FALSE).

4. "Can be" → just one value needs to fit (one example = TRUE).

5. "Cannot be" → look for any counterexample (one counterexample = FALSE).

The key idea: three faces reveal three dimensions

A rectangular prism has three dimensions: length (L), width (W) and height (H).

Each face shows two of these dimensions as a grid of squares. Count the columns (across) and rows (down) of each face.

Step 1 — Count the grid squares in each face

Step 2 — Match up the three dimensions

Look for numbers that appear in two faces — each such number is one dimension of the prism.

• 4 appears in Face A and Face B → one dimension is 4
• 3 appears in Face A and Face C → one dimension is 3
• 2 appears in Face B and Face C → one dimension is 2

So the prism is 4 × 3 × 2.

Step 3 — Count the cubes (volume)

Think of the prism as stacked layers:

Bottom layer (4 × 3):
+--+--+--+--+
|  |  |  |  |
+--+--+--+--+    × 2 layers tall
|  |  |  |  |
+--+--+--+--+

Bottom layer = 4 × 3 = 12 cubes
Total = 12 × 2 = 24 cubes

Answer: 24

Check with the shortcut formula

Volume = √(Area A × Area B × Area C) = √(12 × 8 × 6) = √576 = 24 ✓

Common trap: multiplying face areas together

12 × 8 × 6 = 576 is wrong. This multiplies each dimension twice (giving Volume²). Always find the three individual dimensions first, then multiply them once.

Repeatable checklist

1. Count the columns and rows of each face.

2. Find which number appears in two faces — that is one dimension.

3. Do this for all three dimensions.

4. Multiply: L × W × H.