AR Type 3 Patterns

Explanation

The correct answer is C – The top triangle must be flipped horizontally (as in C and D). The top half should contain a circle, not an oval (reflecting the rounding of the square, not a rectangle).

Pattern: The shapes in the top and bottom halves swap positions. The shape from the top half is flipped horizontally, whilst the shape from the bottom half is flipped vertically (or rotated 180 degrees) and rounded off.

Method: Focus on the obvious point of similarity, namely that the triangle in the top half of Box 1 appears upside-down in the bottom half of Box 2. This makes it easier to deal with the bottom half of Box 1, which correspondingly gets moved into the top half of Box 2, only that it gets flipped vertically, and rounded off.

Explanation

The correct answer is D – We are looking for shapes with 2 regions in every position other than the bottom-right, where we are looking for a shape with 4 regions.

Pattern: The shape in each position gets one additional internal region. The shape itself can change.

Method: Observe that the “shapes” (even though they change) with the most internal regions in Box 1 also have the most internal regions in Box 2 – the shape in the top-right goes from two to three, whilst the shape in the bottom-left goes from one to two. All in all, it should soon become clear that the shape in each position gains one internal region. You should expect each shape to change, though there’s nothing to suggest that this must happen.

Explanation

The correct answer is A – We seek a square inside a rectangle, as in A, B and C. However, the bottom rectangle should look identical because it will be flipped horizontally. This means A must be the correct answer, revealing that the pattern is for colours to switch between white and black.

Pattern: The top shape ends up inside a larger version of the bottom shape, which is inverted. The question alone does not make it clear whether the shapes swap colours with each other or merely swap between white and black – however, we can tell this from the available answers.

Method: Concentrate on Shape first – clearly, the top shape ends up inside the bottom shape, although, as is explained above, you cannot tell without the answer options what the rule on Colour is.

Explanation

The correct answer is A – Top half: 4 and 8; bottom half: 3 and 7.

Pattern: The two shapes in the top half gain a side; those in the bottom half lose a side.

Method: We go from four white shapes in Box 1 to four white shapes in Box 2, and none of the shapes remains the same per se. Thus, it seems reasonable to ignore Size, Position, Orientation and Colour. Focussing on Number/Shape, then, the pattern should soon reveal itself.

Explanation

The correct answer is C – The answer must have only white pentagons and only white triangles – only C satisfies this (along with the other conditions of the pattern.

Pattern: The top shape elongates horizontally, staying in position and containing copies of the two shapes in the bottom half. Meanwhile, one of the shapes in the bottom half contains a vertically-elongated version of the top shape. Finally, the shape from the bottom half changes colour between white and black, whilst the shape from the top half retains its colour.

Method: Confusing as the pattern seems, the best we can do is to focus on what is inside Box 1 and where it ends up in Box 2. A rounded shape appears twice in Box 2, and only once in Box 1, and so we can infer that the shape in the top half gets stretched horizontally, whilst a vertically-elongated version (or better, a horizontally-compressed version) of the top shape appears in the bottom half of Box 2. Focussing then on the identical shapes in the bottom half, they evidently change colour, and appear internally in Box 2’s top half and externally in Box 2’s bottom half.

Explanation

The correct answer is B – Only C and D have the right shapes in the right positions. In D, every shape’s colour changes, rather than all shapes excluding the left-middle and right-middle positions. 

Pattern: The three shapes along the top-left-to-bottom-right diagonal rotate slightly clockwise. The two leftmost shapes along the bottom row swap positions with the two rightmost shapes along the top row. Every shape changes colour between black and white, except for those in the left-middle and right-middle positions.

Method: Isolate the larger shapes along the top-left-to-bottom-right diagonal – evidently, these rotate and switch between white and black. Of the remaining shapes, those in the middle-left and middle-right positions do not change; the last four swap shape and colour. 

Explanation

The correct answer is D – The outer black square will become the innermost shape, followed by the white circle, black circle and grey square.

Pattern: Every shape moves outwards one position, the outermost shape coming into the innermost spot.

Method: Concentrate on the outermost shape in Box 1, the grey heart, which ends up innermost in Box 2. This is the key to identifying this very characteristic Type 3 Question pattern.

Explanation

The correct answer is B – Only B and C feature the correct changes to the central shape. However, in C, the black triangle has rotated inappropriately, and the hexagon has not gained any sides.

Pattern: The whole structure rotates 90 degrees anticlockwise. Taking the central shape to be the base of the structure, the shape projecting from its right side does not change, only rotating in keeping with the whole structure. Meanwhile, the central shape swaps with the element inside it, and their colours swap. Finally, the shape projecting from its left side gains two sides.

Method: Focus on the whole structure – which evidently rotates anticlockwise – and then each of its components. The central element inverts with respect to Shape, the shape projecting from its right side doesn’t change, and the shape projecting from its left side increases in complexity – you might guess that it gains two sides, but you will have to look at the answer options to know for sure.

Explanation

The correct answer is D – There should be no white circle, as it is the second-innermost in the original. This immediately eliminates every option but the answer.

Pattern: The second-innermost shape is removed, and then every shape moves one position inwards, the innermost shape taking up the outermost position.

Method: The relative simplicity of Box 2 should encourage you to notice that one shape from Box 1 will be lost. The innermost shape, the white heart, becomes outermost, indicating a classic inward shift. Then, all that remains is to identify the loss of the grey diamond, i.e. the second-innermost shape.

Explanation

The correct answer is C – Only B and C have the hour hand appropriately positioned, while only A and C have the minute hand appropriately positioned.

Pattern: The minute hand rotates 90 degrees anticlockwise, whilst the hour hand rotates 90 degrees clockwise.

Method: As with all clock patterns, your first thought should be to ignore the time that is told, concentrating instead on each hand and/or the angle between them. The most obvious transformation from Box 1 to Box 2 is the 90-degree clockwise shift in the hour hand, from the 3 o’clock to the 6 o’clock position. Then, focus on the minute hand, which evidently does the opposite, rotating 90 degrees but in the anticlockwise direction.

Explanation

The correct answer is A – A is the only option with appropriate colouration – B and D have reflected the colour arrangement vertically, not horizontally.

Pattern: The shape arrangement is reflected vertically; the colour pattern is reflected horizontally. Imagine 2 lines of symmetry, then focus on the colour and shapes individually to see how this works. This is a particularly hard question, so don’t be disheartened! You’re doing amazingly. 

Method: Since Box 2 still contains a 4-by-4 group of circles and squares both black and white, we should try to isolate different patterns in turn. The easiest to spot is the Colour pattern, which simply gets flipped upside-down. As far as Shape/Position goes, it is best to concentrate on squares, of which there are fewer than circles. You will notice that the squares in the top-right end up in the top-left in Box 2, and that those in the bottom-left end up in the bottom-right – in other words, Position gets flipped laterally, rather than upside-down.

Explanation

The correct answer is C – We seek a shape with seven sides and three regions.

Pattern: The shape itself gains a side, whilst the number of regions decreases by one.

Method: The question visibly encourages you to look for a pattern involving the number of regions, which decreases from three in Box 1 to two in Box 2. On the other hand, you should expect an additional pattern, which is likely to come from the overall shape itself, and indeed, its number of sides increases by one, from four to five. Of course, you could be wrong, and the pattern could be something quite different, but it is worth checking the answer options to find out!

Explanation

The correct answer is D – B has the wrong combination of shapes. C has the wrong pattern in the rightmost shape. A is wrong because the shape should not be rotated, only the internal pattern, which happens to be plain white.

Pattern: The shapes rotate in an anticlockwise direction. The patterns rotate in a clockwise direction. The pattern that occupies the topmost position originally (and rightmost subsequently) is rotated clockwise slightly.

Method: Ignore Box 3, as the transformation is designed to be more confusing than in the example case. Focussing on the simplest characteristics should help here, namely the overall shapes – we have a triangle, square and circle, and these evidently move in anticlockwise rotation. The diagonal patterning suggests that the visual pattern is likely to be involved rather than the number of subdivisions. The cross moves clockwise, as do the other two patterns, only that the diagonal lines are either reflected or rotated – you must defer to the answer options.

Explanation

The correct answer is B – The grey circle will now be second-innermost, and the white triangle will now be outermost. The white triangle should still point upwards; the circle cannot visibly change orientation; the arrow will point down.

Pattern: The outermost and second-innermost shapes swap position with one another. The originally-outermost (now-second-innermost) and innermost shapes flip horizontally.

Method: Concentrate on the easiest shape to identify, which for most people will be the white heart. It does not change colour, but gets flipped horizontally and ends up second-innermost. However, the innermost black triangle does not move position, only flipping horizontally – this indicates that there is not a uniform change in position, but rather a swap between two shapes, which you can confirm to be the outermost and second-innermost. Finally, you should check that the second-outermost shape remains unchanged.

Explanation

The correct answer is D – A: the three rectangles are in the wrong positions.

B: the upper-central hexagon and central have swapped positions.

C: the central shapes have swapped to opposite sides of the pentagon.

Pattern: Lateral inversion (i.e. vertical reflection).

Method: This rule is easy to spot, and harder to apply – the difficulty lies in identifying the correct answer. You should be wary of alternative reflections, rotations, and missing or moving shapes.

Explanation

The correct answer is A – There should be a white circle in the centre. The surrounding triangles should be rotated 45 degrees, not 60 (or 180) as in C. Finally, the colour-swapping should leave two greys uppermost.

Pattern: The central and peripheral shapes swap positions/sizes. The shape occupying the central position takes up the colour of the originally-central shape. The colours of the peripheral shapes swap with those of their diagonally-opposite corners. Finally, the peripheral shapes are rotated by 45 degrees.

Method: You should be quick to observe that the main pattern simply involves swapping the Position and Size of the large central shape with the four smaller shapes. However, you should expect the central shape to the rotated. As for the Colour pattern, this is evidently unchanged for the largest, central element, whilst the pattern amongst the four smaller shapes involves swapping opposite corners (or, expressed differently, a 180-degree rotation).

Explanation

The correct answer is B – We expect the square, arc, crescent and heart to disappear. C has erroneously replaced the pentagon with a hexagon.

Pattern: The shapes with an even number of sides are removed.

Method: You should notice that no shapes change in any way, with respect to Size, Position, Orientation or Colour. All that happens is that some are removed. Since Box 1 and Box 3 do not have comparable positional arrangements, you should be drawn to look for a pattern that relates to an intrinsic property amongst the removed shapes. Since these are a hexagon, a rectangle and an arrowhead, your instinct should be to look for an answer option in which the even-sided shapes from Box 3 are removed (in order to confirm the pattern).

Explanation

The correct answer is D – We seek a triangle in the top half and the rectangle (approximating a square) in the bottom half.

Pattern: The original shape is halved, keeping only its top half. Then, a rectangle is formed to match the width and height of the remaining shape, in the bottom half.

Method: When the pattern seems odd, as though it could involve several plausible rules, all you can do is focus on Box 1 and see how you might generate Box 2 from it. Since all Box 1 contains is a circle, you can infer that halving the shape in Box 3 will generate the shape in the top half of Box 4. As it so happens, only one answer option matches this rule, confirming that the shape in the bottom half takes the form of a rectangle that matches the largest dimensions of the shape in the top half.

Explanation

The correct answer is C – Two four-sided shapes should become four two-sided shapes. Only A and C contain two-sided shapes, but A only has three copies.

Pattern: The number of sides on the repeated shape swaps with the number of copies of the shape, e.g. three five-sided shapes becomes five three-sided shapes.

Method: Although this is an unusual pattern, it’s fair to say that there are only so many ways you might be able to generate Box 2 as shown from Box 1. Pentagons are very often involved in Number-based rules, and this pattern is no different.

Explanation

The correct answer is D – There should be four rectangles/squares in the same pattern as the pentagons as the top right box of the question, and the remaining shapes should be triangles. Meanwhile, the colouration should be as in B and D.

Pattern: Four shapes in a specific configuration gain a side, whilst the others lose a side. Every white shape becomes black, and vice versa, without exception.

Method: The Colour change is the easiest to spot, and can then be ignored. Every shape is the same in Box 1, but this is not true of Box 2, and in fact, none of them is the same as in Box 1. A pattern based on the Position and involving the number of sides seems the most likely, and this can be checked by looking at the possible solutions.

Explanation

The correct answer is C – We are looking for a black circle within a grey diamond, inside a grey triangle within a white square.

Pattern: The outer two shapes become the inner two shapes (the outer of the two still the outer, and the inner still the inner) – and the reverse for the inner pair. In other words, the square within the circle is now inside the pentagon within the triangle.

Method: As with all patterns of this type, focus on each element in turn. Every shape in Box 1 is present in Box 2 with no change to Colour or Orientation. Thus, you can predict a pattern involving only Position. Now, the white circle goes from outermost to second-innermost, whilst the grey square goes from second-outermost to innermost; tracking each shape in this way reveals that the outer and inner pairs essentially swap position.

Explanation

The correct answer is A – We expect the ten-sided star and the four-sided rectangle to disappear.

Pattern: Of the six shapes, the one with the most sides and the one with the fewest sides are removed.

Method: Two shapes are removed – but from our available answer options, this evidently doesn’t relate to Position. An astute candidate should spot the relevant features of the circle and the cross that lead to their removal.

Explanation

The correct answer is C – The white pentagon will become grey – that immediately eliminates three of the four options.

Pattern: This is just a question of colour: white shapes become grey, grey shapes become black, and black shapes become white.

Method: Quite clearly, there is no change to Size, Position, Orientation, Number or Shape. All you have to focus on, therefore, is Colour. 

Explanation

The correct answer is D   2 + 5 + 3 = 10 – so we need a five-pointed star that contains a heart, surrounded by four pentagons, as in D.

Pattern: A central shape appears whose number of sides equals the total number of sides in the original box. Moreover, the central shape contains a copy of the shape in the top left of the original box, and each corner of the resultant box contains a copy of the shape in the top right of the original box.

Method: Two of the three shapes in Box 1 are present in Box 2, namely the square and the circle. What happens to these is fairly clear, and could either be based on Position or Number (of sides). Looking at the answer options, you must evidently work out how the large, many-sided central shape is generated. Given its many sides, summing the sides in Box 1 seems like a reasonable rule to test, and indeed, this holds for the eight-pointed star. 

Explanation

The correct answer is A – Top left: 1 to 2 – top right: 6 to 3

Bottom left: 3 to 6 – bottom right: 1 to 2

Pattern: Each box contains four shapes, and the shapes themselves do not stay the same – but if the number of regions in the original shape is odd, its replacement has double the number of regions. Conversely, if the number of regions in the original shape is even, its replacement has half the number of regions.

Method: You will know, by now, to suspect that the number of regions is relevant. Assuming, first, that Position is unchanged, note that four becomes two, two becomes four, three becomes six, and five becomes ten – from these data, the pattern is readily deduced.