Solving Analogy Questions

Type 3 analogy questions test a distinct skill: your ability to identify a transformation from one shape to another and then apply that same transformation to a new shape. This lesson provides a step-by-step method for solving these questions reliably, with extensive worked examples.

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The Step-by-Step Method

Step 1: Examine Shape A

Note everything about it:

• What shape(s) are present?
• What colour/shading?
• What size?
• What orientation?
• How many elements?
• Where are they positioned?

Step 2: Examine Shape B

Note the same features.

Step 3: Identify Every Difference

Compare A to B. List every difference you can see:

• Did the shape rotate? By how much?
• Did the colour change? From what to what?
• Did the size change?
• Was something added or removed?
• Was the shape reflected?

Step 4: Describe the Transformation

Formulate a clear statement: "A was [transformed] to become B."

Example: "A was rotated 90° clockwise and changed from black to white."

Step 5: Apply the Same Transformation to C

Take Shape C and apply every part of the transformation:

• Rotate C by the same angle and direction
• Change C's colour in the same way
• Change C's size in the same way
• Add or remove the same elements

Step 6: Match to Answer Options

The result should match one of the four options. Select it.

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Worked Example 1: Rotation Only

A: A right-angled triangle with the right angle at the bottom-left, hypotenuse running from top-left to bottom-right. Shaded black.

B: The same triangle rotated 90° clockwise — right angle now at the bottom-right. Still black.

Transformation: 90° clockwise rotation. No colour, size, or other changes.

C: An L-shape oriented with the long arm pointing up and the short arm pointing right.

Apply transformation to C: Rotate the L-shape 90° clockwise → long arm now points right, short arm points down.

Select the option showing this rotated L-shape.

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Worked Example 2: Colour Inversion

A: A large circle containing a small triangle. The circle is black, the triangle is white.

B: A large circle containing a small triangle. The circle is white, the triangle is black.

Transformation: Colour inversion — black becomes white, white becomes black. No change in shape, size, or position.

C: A large square containing a small circle. The square is black, the circle is white.

Apply transformation to C: The square becomes white, the circle becomes black.

Select the option showing a white square containing a black circle.

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Worked Example 3: Reflection + Size Change

A: A small arrow pointing to the upper-right (↗).

B: A large arrow pointing to the upper-left (↖).

Transformation: Two changes:

1. Reflection across the vertical axis (right→left, creating a mirror image)
2. Size change from small to large

C: A small arrow pointing to the lower-right (↘).

Apply transformation to C:

1. Reflect: lower-right becomes lower-left (↙)
2. Size: small becomes large

Select the option showing a large arrow pointing to the lower-left (↙).

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Worked Example 4: Addition + Colour Change

A: One black circle.

B: Two grey circles (the original circle changed to grey, and a second grey circle was added).

Wait — was the original circle changed to grey AND a new grey circle added? Or were both always grey? The transformation must be unambiguous.

Revised: A: One black circle. B: One grey circle, one black circle (the original changed from black to grey, and a new black circle was added).

Transformation:

1. The existing shape changes from black to grey
2. A new black shape (same type) is added

C: One black triangle.

Apply transformation to C:

1. Existing triangle: black → grey
2. Add a new black triangle

Result: One grey triangle, one black triangle.

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Worked Example 5: Multiple Simultaneous Transformations

A: A small black square in the top-left corner of the box.