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### Non-Verbal Reasoning

**Next in the Series **

Choose the option (A, B, C, D or E) that completes the sequence in the simplest and most logical way.

**Answer: (D)**

The figure rotates 90° clockwise with each subsequent step in the sequence. With each step, two of the shaded segments swap places. From the first step to the second, the crisscross and white segments swap places; from the second to the third, the crisscross and chequered segment swap places; from the third to the fourth, the black and the crisscross segment swap places. Thus, when the figure has the segments with their longer sides horizontal, the top two segments swap; when the longer sides are vertical, the middle two segments swap. The figure has the longer sides of the segments vertical in the fourth step, so the middle two segments will swap; when the figure rotates 90° clockwise, the white segment will be on top, followed by black, then chequered, then crisscross. The answer is therefore (D).

**Answer: (C)**

The central arrow is pointing at the vertices of the hexagon; it rotates one position anticlockwise, then two positions clockwise, then three positions anticlockwise. Thus, the arrow must rotate four positions clockwise in the correct answer, so that the white arrow is pointing at the lower-right vertex of the pentagon. Eliminate (A), (B) and (D). The two remaining answers have the ring and the star in the same positions, and the ring is grey in both; the only difference is the colour of the star. The star alternates between white, grey and black before repeating the sequence. Since the star in the fourth step is white, the star in the correct answer should be grey. Answer (C) is correct. For the record: The ring alternates between grey and black; it moves around the outer sides of the pentagon, one position clockwise with each step. The star also moves around the outer sides of the pentagon, but it moves one additional position anticlockwise with each step, so it moves one position on the first move, two positions on the second move, and three on the third move. Thus, the star must move four positions to its position in the correct answer.

**Missing Segment **

Choose the option (A, B, C, D or E) that completes the image in the simplest and most logical way.

**Answer: (D)**

There are quite a lot of elements in this sequence. Perhaps the simplest to see are the colours, which are consistent within each row. In the top row, the lower-right shape is black, the upper-left shape is white, and the other two shapes are grey; in the middle row, the upper-right shape is black, the upper-left shape is grey, and the other two shapes are white; in the bottom row, the upper-left shape is black and the other shapes are white. On this basis, eliminate (A), (C) and (E), as there are no grey shapes in the bottom row. In the bottom row, the explosion is in the upper-right position in the left box, then in the upper-left in the middle box; thus, it must rotate one further position anticlockwise, to the lower-left, in the correct answer. The answer is therefore (D).

**Answer: (E)**

There are various shapes in each box, and the shapes in each upper box depend on the two boxes directly beneath it: anything in common in the two lower boxes is not included, but anything unique to the two lower boxes is combined. For example, the right-hand box in the second row from the top contains all the shapes in the pyramid; the box next to it includes only the circle and the smaller, inner diamond; these two (common to both boxes) have been removed from the top box, which includes all the other shapes that were unique to the righthand box. You must work from the boxes above the missing segment, along with those next to it, to work out what it must contain, and also what it cannot contain. The middle box in the third row includes the crossing lines, as does the third box in the bottom row; thus, these cannot appear in the correct answer, as otherwise they would not be in the middle box in the third row. Eliminate (B) and (D). The middle box in the third row also contains the circle and the larger diamond, which are not in the third box in the bottom row; thus, they must be in the correct answer. Eliminate (C). Finally, the third box in the bottom row includes the smaller, inner diamond, which is not in the middle box of the third row; thus, it must also be in the missing segment, so that it is eliminated in the middle box in the third row. The answer is therefore (E). For the record: You could doublecheck against the left-hand box in the third row and the left-hand box in the bottom row, if you wanted to confirm the contents of the missing segment.

**Middle of the Sequence**

In this question, the five images can be rearranged into a logical sequence.

Choose the option (A, B, C, D or E) that occurs in the middle position of the simplest and most logical sequence.

**Answer: (B)**

The figure in each answer choice consists of seven segments, either black or white; there are four black segments and three white segments, and the colours appear to move up or down the figure by one position with each step of the sequence. It‟s probably easiest to work out the overall sequence by focusing on the two adjacent black segments, which are the top two segments in (A), the bottom two in (B), and so on; in (D), they are the top and bottom, indicating that the colours repeat up/down the sequence, with the bottom colour moving to the top (or vice versa). Starting from (B) and following the adjacent black segments up the figure, we can see that BCE (or ECB) must be part of the sequence, depending whether the colours move up (BCE) or down (ECB). However, there is no option of a figure with the third and fourth segments from the top both black, which would have to come after (E) if the sequence involves the colours moving up the figure. Thus, the colours must move down the figure, with the bottom colour moving to the top; this also means that (E) must be the first in the sequence, since nothing can come after it, and it has to be in a block of BCE or ECB. (B) is therefore the middle of the sequence, and the correct answer. For the record: The complete sequence is ECBDA. While (D) is the one answer that makes it clearest that there are seven segments in the figure, it is also the most challenging to fit into the sequence, since the two black segments that are adjacent in the other four answers are at the top and bottom in (D).

**Answer: (A)**

Each figure consists of a stack of shapes: a diamond atop a Q-shape atop a curved arrow. The shapes are always stacked in this order; however, the Q-shape and the arrow rotate, and the shadings change with each step in the sequence. There are a total of four possible shadings: striped, white, wavy and grey. Two answers, (B) and (E) have the same three shadings in the same order – wavy atop grey atop striped; thus, these are likely the first and last in the sequence – since it‟s a sequence involving four shadings, each shape would repeat its first shading on the fifth step. The rotation of the Q-shape is likely the easiest to see; it rotates 90° anticlockwise with each next step. This deduction proves that (B) and (E) are the first and last steps (though not clear yet which is which), since the Q-shape would end up in the original orientation after rotating 4 times. Thus, the second to fourth steps are (D), (A) and (C), as the Q-shape has rotated 90°, 180° and 270° anticlockwise, respective to its original orientation, through those three answers. (A) is the middle of the sequence, so it‟s correct. For the record: Once you work out the second to fourth steps based on the Q-shape, you can see that the curved arrow rotates 45° clockwise with each step; thus, the overall sequence is BDACE. Knowing this, you can also see that the shadings move up the stack of shapes, with the shading of the diamond disappearing during the next step, only to reappear on the bottom as the arrow‟s shading in the following step. However, on Test Day, these deductions would not be necessary, as you only need do as much work as required to determine the middle of the sequence. On many questions, you will be able to work out the middle of the sequence without knowing the exact overall sequence.