Figure series, analogy, classification, mirror and water images, paper folding, and embedded figures
Here the data are figures, not words, but the logic is the same as in verbal reasoning: find the rule that transforms one figure into the next. Because this note cannot display pictures, each pattern is described precisely in words; practise it against the figure sets in any standard reasoning book.
| Sub-type | What changes between figures |
|---|---|
| Figure series | Rotation, addition or removal of elements, movement of a marker |
| Figure analogy | The change in A to B, applied to C to give the answer |
| Figure classification | The shared property all but one figure have |
| Mirror image | Left and right swap; top and bottom stay |
| Water image | Top and bottom swap; left and right stay |
| Paper folding and punching | Each fold doubles the holes by reflection across the fold line |
| Embedded figures | Find the given simple shape hidden, unrotated, inside a complex figure |
A clockwise rotation moves the top of a figure towards the right; an anticlockwise rotation moves the top towards the left. Common series steps are 45° or 90° per figure. To predict the next figure, apply the same angular step again in the same direction.
Imagine a vertical line to the right of the figure. The image is left-right reversed: a shape pointing left now points right, and the letters b and d swap, as do p and q. Vertically symmetric letters (A, H, I, M, O, T, U, V, W, X, Y) look unchanged in a vertical mirror.
Imagine a horizontal line below the figure. The image is top-bottom reversed: an arrow pointing up now points down, and the letters b and p swap, as do d and q. Horizontally symmetric letters (B, C, D, E, H, I, K, O, X) look unchanged in a water image.
A square sheet folded once and punched gives, when unfolded, holes that are mirror images across the fold line. Each fold doubles the number of holes: one fold then one punch gives 2 holes; two folds then one punch gives 4 holes, arranged symmetrically about both fold lines.
A series shows an arrow that points up, then right, then down. The arrow has turned 90° clockwise each time. The next figure shows the arrow pointing left.
A square contains 1 dot, then 2 dots, then 3 dots in successive figures. The rule is "add one dot each step", so the next figure has 4 dots.
If a triangle pointing up becomes a triangle pointing down (a 180-degree flip), then a triangle pointing right, under the same flip, becomes a triangle pointing left.
The mirror image of the word "POLICE" (vertical mirror) reverses the letter order and flips each letter left-to-right, so it reads as a reversed "ECILOP" with each letter mirrored. The symmetric letters O and I look the same; P, L, C, E appear reversed.
The water image of "1996" flips each digit top to bottom and keeps the order. The digit 1 and the symmetric forms change least; 9 becomes a 6-like shape and 6 becomes a 9-like shape because the loop moves to the opposite end.
A square sheet is folded once along the vertical centre line, and a single hole is punched near the top-left of the folded sheet. When unfolded, there are 2 holes, symmetric about the vertical centre line, one near the top-left and one near the top-right.
A simple right-angled triangle is to be found inside a complex grid figure. Scan the complex figure for the triangle in its given orientation (do not rotate it); the correct option contains the triangle exactly as shown, formed by existing lines of the complex figure.