Figure analogy and classification for AFCAT: find the change, then apply it

Figure analogy is the non-verbal cousin of "Doctor : Hospital :: Teacher : ?". You see figure A turn into figure B, then figure C and a blank. The answer is whatever C becomes under the same change. Figure classification flips it round: five figures, four of which obey one rule, and you pick the one that does not.

Both reward the same skill: stating the change precisely. "It flipped" is not precise enough, because a flip and a half-turn often look alike on one element and differ on another. This guide gives you the vocabulary, the tests that separate look-alike rules, and practice items that are fully described in text.

How figures are described here

Positions are cells on a 3×3 grid, numbered like a phone keypad: 1, 2, 3 across the top, 4, 5, 6 across the middle, 7, 8, 9 across the bottom. Arrows use compass directions, with north at the top of the box.

It helps to know where each cell goes under the common transformations.

You do not need to memorise this. Work it out once by imagining the grid turning, and the pattern sticks: under a 90° clockwise turn, the top row becomes the right column.

The common transformations

A single pair can show two changes at once, for example a rotation plus a shading swap. Look for the second change once you have found the first.

Rotation or reflection? The test that decides

A mirror image and a rotation can move a corner dot to the same cell. What separates them is anything with a direction: an arrow, a flag, the letter F.

• A rotation turns the arrow as well as moving it.
• A reflection flips the arrow across the mirror line.

So when the first pair could be read as either, look at the directional element and check which rule produces it.

Worked analogies

Example 1: rotation, not reflection. Figure A has an arrow in cell 1 pointing north and a dot in cell 9. Figure B has an arrow in cell 3 pointing east and a dot in cell 7. Figure C has an arrow in cell 7 pointing west and a dot in cell 2. What is figure D?

• A 90° clockwise turn sends cell 1 to cell 3 and cell 9 to cell 7, and turns north into east. That fits A to B completely.
• A left–right mirror would also send 1 to 3 and 9 to 7, but the arrow would still point north. So it is rotation.
• Apply it to C: cell 7 goes to cell 1, west turns to north, and cell 2 goes to cell 6.
• D: an arrow in cell 1 pointing north, and a dot in cell 6.

Example 2: inside–outside swap. Figure A is a large square with a small circle inside it. Figure B is a large circle with a small square inside it. Figure C is a large triangle with a small pentagon inside it.

• The inner and outer shapes swap. D: a large pentagon with a small triangle inside it.

Example 3: shading swap. Figure A is a shaded circle inside an unshaded square. Figure B is an unshaded circle inside a shaded square. Figure C is a shaded triangle inside an unshaded circle.

• The shapes stay put and the shading swaps. D: an unshaded triangle inside a shaded circle.

Example 4: two counts swap. Figure A has 3 dots and 1 line. Figure B has 1 dot and 3 lines. Figure C has 4 dots and 2 lines.

• The number of dots and the number of lines swap. D: 2 dots and 4 lines.

Figure classification

Five figures are shown. Four share a rule. Find the fifth.

What to check, in this order:

1. Is each figure a rotation of the others? If four are rotations of one figure and one is a mirror image, that is your answer.
2. Counts. Lines, sides, dots, intersections, shaded parts.
3. A relation between two counts. For example, dots = sides − 2.
4. Position. Where the small element sits relative to the large one.
5. Open or closed; straight or curved; symmetric or not.

Example 5: the mirror among rotations. Each figure is the letter F in a different orientation. An upright F is a vertical stroke with two short strokes pointing right, at the top and the middle.

• (a) Upright F.
• (b) Vertical stroke with two short strokes pointing left, at the bottom and the middle.
• (c) Horizontal stroke with two short strokes pointing down, at the right end and the middle.
• (d) Vertical stroke with two short strokes pointing left, at the top and the middle.

Test each against the upright F:

• (b) is the upright F turned 180°. The top moves to the bottom and right-pointing strokes point left. It is a rotation.
• (c) is the upright F turned 90° clockwise. The vertical stroke lies flat, the top end moves to the right, and the strokes point down. It is a rotation.
• (d) keeps the strokes at the top but points them left. That needs a flip, not a turn.
• Odd one out: (d), the mirror image.

Example 6: a relation between counts. A triangle with 1 dot inside, a square with 2 dots, a pentagon with 3 dots, a hexagon with 4 dots and a heptagon with 6 dots.

• In four figures, dots = sides − 2. The heptagon should have 5.
• Odd one out: the heptagon.
• Rival check: no figure is the only one with an even or odd number of dots, so no second property picks out a different answer.

Practice set

1. Figure A has a dot in cell 1 and a cross in cell 2. Figure B has a dot in cell 9 and a cross in cell 8. Figure C has a dot in cell 4 and a cross in cell 3. What is figure D?
2. Figure A is a flag: a vertical pole with a triangular flag at its top pointing right. Figure B is the same pole with the flag at its top pointing left. Figure C is an arrow in cell 4 pointing north-east. What is figure D?
3. Figure A is a large shaded square with a small unshaded circle inside. Figure B is a large unshaded circle with a small shaded square inside. Figure C is a large unshaded triangle with a small shaded pentagon inside. What is figure D?
4. Odd one out. Each figure is an arrow with a small circle beside it. (a) Arrow pointing north, circle to its east. (b) Arrow pointing east, circle to its south. (c) Arrow pointing south, circle to its west. (d) Arrow pointing west, circle to its south.
5. Odd one out. (a) A closed circle. (b) A closed square. (c) An open arc. (d) A closed triangle.

Answers:

1. A dot in cell 6 and a cross in cell 7. A to B is a 180° turn: cell 1 goes to 9 and cell 2 goes to 8. A water image would send cell 1 to 7, and a mirror would send it to 3, so neither fits. Under 180°, cell 4 goes to 6 and cell 3 goes to 7.
2. An arrow in cell 6 pointing north-west. The flag stays at the top but points the other way, so this is a left–right mirror, not a 180° turn (which would put the flag at the bottom).
3. A large shaded pentagon with a small unshaded triangle inside. The shapes swap places, and each keeps its own shading.
4. (d). In the others, the circle is on the arrow's right-hand side as the arrow travels. For an arrow pointing west, its right is north, but the circle is to the south. (a), (b) and (c) are rotations of one figure; (d) is its mirror image.
5. (c), the open arc. The rest are closed figures.

What to do next

• Draw the cell table above from memory once. Then check two or three rows by imagining the grid turning.
• For every analogy you solve, write the rule as one sentence before looking at the options.
• Do 10 analogies and 10 classifications a day for a week, and mark which transformation each used.
• Continue with figure series, then mirror and water images, where the reflection rules here are used on letters and clocks.