Layering & Combining

In Layering and Combining questions, you are given two or more shapes that are placed on top of each other (overlaid), and you must work out what the final combined image looks like. Think of it like stacking transparent sheets of paper — you can see through to the layers below.

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How Layering Works

When two shapes are layered (placed on top of each other), the result shows everything from both shapes. If Shape A has a circle on the left and Shape B has a square on the right, the combined image has both a circle on the left and a square on the right.

Simple Layering

Shape A:          Shape B:          Combined:
+--------+        +--------+        +--------+
|  O     |   +    |     □  |   =    |  O  □  |
|        |        |        |        |        |
+--------+        +--------+        +--------+

The circle and square simply appear together in the combined image because they do not overlap.

Overlapping Layering

When shapes overlap (occupy the same space), the result depends on the rules of the question:

Rule 1: Simple overlay (both visible)

Shape A:          Shape B:          Combined:
+--------+        +--------+        +--------+
|  ____  |        |   __   |        |  ____  |
| |    | |   +    |  /  \  |   =    | | /\ | |
| |____| |        |  \__/  |        | |/  \| |
+--------+        +--------+        | |\__/| |
                                    | |____| |
                                    +--------+

Both the rectangle and the circle are visible, with the circle appearing inside the rectangle.

Rule 2: Shading interaction

When a black area overlaps a white area, different rules may apply:

• Black covers white: The black area dominates.
• XOR rule: Where both are black, the result becomes white (they cancel out). Where only one is black, the result stays black.

The question will usually make it clear which rule applies, or you can work it out from the examples given.

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Types of Combining Questions

Type 1: Which Combined Image Is Correct?

You are shown two or more separate shapes and asked which option shows them correctly combined.

Example:

Shape A: A vertical line in the centre of a box
Shape B: A horizontal line in the centre of a box

Combined: A plus sign (+) in the centre of a box

Type 2: Which Two Shapes Combine to Make This Image?

You are shown a combined image and asked which pair of separate shapes would create it.

Example:

Combined image: A circle with a diagonal line through it

Which two shapes make this?
Option 1: A circle + a diagonal line       ← Correct!
Option 2: A circle + a horizontal line     ← Wrong (line direction)
Option 3: A square + a diagonal line       ← Wrong (shape is wrong)
Option 4: An oval + a diagonal line        ← Wrong (not a circle)

Type 3: What Is Hidden Underneath?

You are shown the combined image and one of the layers, and asked what the other layer looks like.

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Worked Example 1: Simple Overlay

Shape A:                 Shape B:
+----------+            +----------+
|    △     |            |          |
|          |            |     ○    |
| ○        |            |          |
+----------+            +----------+

What does the combined image look like?

Option 1:               Option 2:
+----------+            +----------+
|    △     |            |    △     |
|     ○    |            |     ○    |
| ○        |            |          |
+----------+            +----------+

Option 3:               Option 4:
+----------+            +----------+
|          |            |    △     |
|    △○    |            |     ○    |
| ○        |            | ○        |
+----------+            +----------+

Analysis:

• Shape A has a triangle at the top-centre and a circle at the bottom-left.
• Shape B has a circle at the middle-right.
• Combined: triangle at top-centre, circle at bottom-left (from A), and circle at middle-right (from B).

Answer: Option 4.

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Worked Example 2: Overlapping Shapes

Shape A: A large white square with a thick border
Shape B: A large white circle with a thick border

Both shapes are the same size, centred on the same point.

What does the combined image look like?