Understand the rule first
List features added, removed and shared. When shapes overlap, count shared boundaries or marks according to the stated rule—once if retained, or not at all if they cancel.
Shape counting & combination 11+ practice
Combine, remove and count visual features without double-counting overlaps.
Overlay two identical squares in exactly the same position. How many squares are visible?
- Both outlines occupy the same location.
- The second does not create a separate visible boundary.
- Only one square outline is visible.
A common misconception
Adding every count automatically even when features overlap or are removed.
Reusable method: List added, removed and unchanged features separately.Question 1 of 8 Non-Verbal ReasoningcoreTwo identical square outlines are overlaid exactly. How many square outlines are visible?
- A0
- B1
- C2
- D4
Need a hint?
Coincident outlines occupy the same visible boundary.
Show worked answer
Answer B: 1
Only one square outline is visible.
Quick method: List added, removed and unchanged features separately.
Question 2 of 8 Non-Verbal ReasoningcoreA triangle is attached to a square along one complete shared side. How many outer edges does the combined outline have?
- A4
- B6
- C5
- D7
Need a hint?
Add all edges, then remove both counts of the internal shared side.
Show worked answer
Answer C: 5
3 + 4 − 2 = 5 outer edges.
Quick method: List added, removed and unchanged features separately.
Question 3 of 8 Non-Verbal ReasoningcoreA figure has 8 dots. Every second dot is removed. How many remain?
- A2
- B3
- C6
- D4
Need a hint?
Removing every second dot removes half of them.
Show worked answer
Answer D: 4
Half of 8 is 4, so 4 remain.
Quick method: List added, removed and unchanged features separately.
Question 4 of 8 Non-Verbal Reasoningexam-styleA diagram contains 7 triangles and 5 circles, with 3 items counted in both groups. How many distinct items are there?
- A9
- B12
- C15
- D35
Need a hint?
Subtract the overlap once after adding both group counts.
Show worked answer
Answer A: 9
7 + 5 − 3 = 9 distinct items.
Quick method: List added, removed and unchanged features separately.
Question 5 of 8 Non-Verbal Reasoningexam-styleOne cell has marks at top and left; another has marks at left and bottom. If shared marks cancel when overlaid, what remains?
- Aleft only
- Btop and bottom
- Ctop, left and bottom
- Dnothing
Need a hint?
The left mark appears twice and cancels.
Show worked answer
Answer B: top and bottom
Only the top and bottom marks remain.
Quick method: List added, removed and unchanged features separately.
Question 6 of 8 Non-Verbal Reasoningexam-styleOne set has 9 items and another has 6, with 4 items in both. How many distinct items are shown?
- A10
- B11
- C15
- D19
Need a hint?
Add both groups and subtract the overlap once.
Show worked answer
Answer B: 11
9 + 6 − 4 = 11.
Quick method: List added, removed and unchanged features separately.
Question 7 of 8 Non-Verbal Reasoningexam-styleTwo identical triangle outlines are overlaid exactly. How many triangle outlines are visible?
- A0
- B2
- C1
- D3
Need a hint?
The boundaries occupy the same position.
Show worked answer
Answer C: 1
Only one triangle outline remains visible.
Quick method: List added, removed and unchanged features separately.
Question 8 of 8 Non-Verbal Reasoningexam-styleA diagram has 10 marks. Three are removed and two new marks are added. How many marks are there now?
- A5
- B8
- C11
- D9
Need a hint?
Apply the removal before the addition.
Show worked answer
Answer D: 9
10 − 3 + 2 = 9.
Quick method: List added, removed and unchanged features separately.